Method for data management and machine learning with fine resolution

ABSTRACT

A method for obtaining a probability in a 3D probability map, includes: obtaining at least one value of at least one parameter for each stop of a 3D moving window, wherein a first, second, third and fourth of the stops are partially overlapped, the first and second stops are shifted from each other by a distance equal to a first dimension of a computation voxel, the first and third stops are shifted from each other by a distance equal to a second dimension of the computation voxel, and the first and fourth stops are shifted from each other by a distance equal to a third dimension of the computation voxel; matching the at least one value to a classifier to obtain a first probability for each stop of the 3D moving window; and calculating a second probability for the computation voxel based on information associated with the first probabilities for the first through fourth stops.

This application claims priority benefit from U.S. provisionalapplication Ser. No. 62/660,271, filed on Apr 20, 2018 and entitled“METHOD FOR DATA MANAGEMENT AND MACHINE LEARNING WITH FINE RESOLUTION”.U.S. Pat. No. 9,922,433 is hereby incorporated by reference in itsentirety.

BACKGROUND OF THE DISCLOSURE Field of the Disclosure

The disclosure relates to a method for data management and machinelearning with fine resolution, and more particularly, to a method offorming a new set of image, data or information with finer resolutionbased on original set of image, data or information obtained fromdetection or analysis instruments, such as camera, microscope (opticalor electronic), endoscope, detector or spectrometer (visible light,fluorescent light, IR, UV or X-ray), ultrasonic machine or system,magnetic resonance imaging (MRI) machine or system, computed tomography(CT) machine or system, position emission tomography (PET) machine orsystem, single-photon emission computed tomography (SPECT) machine insystem, micro-PET machine or system, micro-SPECT machine or system,Raman spectrometer or system, and/or bioluminescence optical (BLO)machine or system, or other machine for obtaining molecular orstructural imaging data.

Brief Description of the Related Art

Big Data represents the information assets characterized by such a highvolume, velocity and variety to require specific technology andanalytical methods for its transformation into value. Big Data is usedto describe a wide range of concepts from the technological ability tostore, aggregate, and process data, to the cultural shift that ispervasively invading business and society, both drowning in informationoverload. Precision medicine is a medical model that proposes thecustomization of healthcare—with medical decisions, practices, and/orproducts being tailored to the individual patient. In this model,diagnostic testing is often employed for selecting appropriate andoptimal therapies based on the context of a patient's genetic content orother molecular or cellular analysis.

SUMMARY OF THE DISCLOSURE

The invention proposes an objective to provide an imaging system using amethod of forming a computational map based on molecular and/orstructural imaging data, such as MRI parameters, CT parameters, PETparameters, SPECT parameters, micro-PET parameters, micro-SPECTparameters, Raman parameters, IR parameters, florescence parametersand/or bioluminescence optical (BLO) parameters, and/or other structuralimaging data, such as from CT and/or ultrasound images, for a firstsubject (e.g., an individual patient). The invention proposes anobjective to provide a method of forming a computational map for opticalor photo imaging of an object (for example photo pictures or videomovies detected by a camera) based on reflection or transmission ofoptical light (electromagnetic waves with wavelength ranges from IR,visible lights, UV and X-ray). The imaging system may comprise adetecting system/device and/or a computing/analyzing system/device. Forexample, the imaging system may be an MRI machine including both thedetecting and computing/analyzing functions. For another example, theimaging system may comprise an MRI machine for the detecting functionand a computer or analyzer for the computing/analyzing function, whereinthe computer or analyzer maybe nearby the MRI machine or in a datacenter of a cloud. The method may build a dataset or database of bigdata containing molecular and/or structural imaging data (and/or otherstructural imaging data) for multiple second subjects and biopsytissue-based data associated with the molecular and/or structuralimaging data for the second subjects. A classifier or biomarker librarymay be constructed or established from the dataset or database of bigdata. The invention proposes a computing method including an algorithmfor generating a voxelwise or pixelwise probability map of a specifictissue or tumor characteristic for the first subject from the firstsubject's registered imaging dataset including the molecular and/orstructural imaging data for the first subject. The computing methodincludes the step of matching the registered ones of the molecularand/or structural imaging data for the first subject to a dataset fromthe established or constructed classifier or biomarker library obtainedfrom population-based information for the molecular and/or structuralimaging (and/or other structural imaging) data for the second subjectsand other information (such as clinical and demographic data or thebiopsy tissue-based data) associated with the molecular and/orstructural imaging data for the second subjects. The method providesdirect biopsy tissue-based evidence (i.e., a large amount of the biopsytissue-based data in the dataset or database of big data) for a medicalor biological test or diagnosis of tissues or organs of the firstsubject and shows heterogeneity within a single tumor focus with highsensitivity and specificity.

The invention also proposes an objective to provide a method of forminga probability change map based on imaging data of a first subject beforeand after a medical treatment. The imaging data for the first subjectmay include (1) molecular and/or structural imaging data, such as MRIparameters, CT parameters, PET parameters, SPECT parameters, micro-PETparameters, micro-SPECT parameters, Raman parameters, and/or BLOparameters, and/or (2) other structural imaging data, such as from CTand/or ultrasound images. The method may build a dataset or database ofbig data containing molecular and/or structural imaging (and/or otherstructural imaging) data for multiple second subjects and biopsytissue-based data associated with the molecular and/or structuralimaging data for the second subjects. A classifier or biomarker librarymay be constructed or established from the dataset or database of bigdata. The invention proposes a computing method including an algorithmfor generating a probability change map of a specific tissue or tumorcharacteristic for the first subject from the first subject's molecularand/or structural imaging (and/or other structural imaging) data beforeand after the medical treatment. The computing method includes matchingthe registered ones of the molecular and/or structural imaging (and/orother structural imaging) data of the first subject before and after themedical treatment in the first subject's registered (multi-parametric)image dataset to the established or constructed classifier or biomarkerlibrary. The method matches the molecular and/or structural imaging(and/or other structural imaging) data for the first subject to theestablished or constructed classifier or biomarker library derived fromdirect biopsy tissue-based evidence (i.e., a large amount of the biopsytissue-based data in the dataset or database of big data) to obtain thechange of probabilities for the response and/or progression of themedical treatment and show heterogeneity of the response and/orprogression within a single tumor focus with high sensitivity andspecificity. The invention provides a method for effectively and timelyevaluating the effectiveness of the medical treatment, such asneoadjuvant chemotherapy for breast cancer, or radiation treatment forprostate cancer.

The invention also proposes an objective to provide a method forcollecting data for an image-tissue-clinical database for cancers.

The invention also proposes an objective to apply a big data technologyto build a probability map from multi-parameter molecular and/orstructural imaging data, including MRI parameters, PET parameters, SPECTparameters, micro-PET parameters, micro-SPECT parameters, Ramanparameters, and/or BLO parameters, and/or from other imaging data,including data from CT and/or ultrasound images. The invention providesa non-invasive method (such as molecular and/or structural imagingmethods, for example, MRI, Raman imaging, CT imaging) to diagnose aspecific tissue characteristic, such as breast cancer cells or prostatecancer cells, with better resolution (resolution size is 50% smaller, or25% smaller than the current resolution capability), and with a higherconfidence level. With data accumulated in the dataset or database ofbig data, the confidence level (for example, percentage of accuratediagnosis of a specific cancer cell) can be greater than 90%, or 95%,and eventually, greater than 99%.

The invention also proposes an objective to apply a big data technologyto build a probability change map from imaging data before and after atreatment. The imaging data may include (1) molecular and structuralimaging data, including MRI parameters, CT parameters, PET parameters,SPECT parameters, micro-PET parameters, micro-SPECT parameters, Ramanparameters, and/or BLO parameters, and/or (2) other structural imagingdata, including data from CT and/or ultrasound images. The inventionprovides a method for effectively and timely evaluating theeffectiveness of a treatment such as neoadjuvant chemotherapy for breastcancer or radiation treatment for prostate cancer.

In order to achieve the above objectives, the invention may provide amethod of forming a probability map composed of multiple computationpixels with the same size or volume. The method may include thefollowing steps. First, a big data database (or called a database of bigdata) including multiple data sets is created. Each of the data sets inthe big data database may include a first set of information data, whichmay be obtained by a non-invasive method or a less-invasive method (ascompared to a method used to obtain the following second set ofinformation data), may be obtained more easily (than the method used toobtain the following second set of information data), or may provideinformation, obtained by a non-invasive method, for a specific tissue,to be biopsied or to the obtained by an invasive method, of an organ(e.g., prostate or breast) of a subject with a spatial volume covering,e.g., less than 10% or even less than 1% of the spatial volume of theorgan of the subject. The organ of the subject, for example, may be theprostate or breast of a human patient. The first set of data informationmay include measured values of molecular and/or structural imagingparameters, such as measured values of MRI parameters and/or CTparameters, and/or other structural imaging parameters, such as from CTand/or ultrasound images, for a volume and location of the specifictissue to be biopsied (e.g., prostate or breast) from the organ of thesubject. The “other structural imaging parameters” may not be mentionedhereinafter. Each of the molecular and/or structural imaging parametersfor the specific tissue may have a value calculated based on an averageof measure values, for said each of the molecular and/or structuralimaging parameters, obtained from corresponding registered regions,portions, locations or volumes of interest of multiple molecular and/orstructural images, such as MRI slices, PET slices, or SPECT images,registered to or aligned with respective regions, portions, locations orvolumes of interest of the specific tissue to be biopsied. Thecombination of the registered regions, portions, locations or volumes ofinterest of the molecular and/or structural images may have a totalvolume covering and substantially equaling the total volume of thespecific tissue to be biopsied. Each of the data sets in the big datadatabase may further include the second set of information data, whichmay be obtained by an invasive method or a more-invasive method (ascompared to the method used to obtain the above first set of informationdata), may be obtained with more difficulty (as compared to the methodused to obtain the above first set of information data), or may provideinformation for the specific tissue, having been biopsied or obtained byan invasive method, of the organ of the subject. The second set ofinformation data may provide information data with decisive, conclusiveresults for a better judgment or decision making. For example, thesecond set of information data may include a biopsy result, data orinformation (i.e., pathologist diagnosis, for example cancer or nocancer) for the biopsied specific tissue. Each of the data sets in thebig data database may also include (1) dimensions related to molecularand/or structural imaging for the parameters, such as the thickness T ofan MRI slice and the size of and MRI pixel of the MRI slice, includingthe width of the MRI pixel and the thickness or height of the MRI pixel(which may be the same as the thickness T of the MRI slice), (2)clinical data (e.g., age and sex of the patient and/or Gleason score ofa prostate cancer) associated with the biopsied specific tissue and/orthe subject, and (3) risk factors for cancer associated with the subject(such as smoking history, sun exposure, premalignant lesions, and/orgene). For example, if the biopsied specific tissue is obtained by aneedle, the biopsied specific tissue is cylinder-shaped with a diameteror radius Rn (that is, an inner diameter or radius of the needle) and aheight tT normalized to the thickness T of the MRI slice. The inventionproposes a method to transform the volume of the cylinder-shapedbiopsied specific tissue (or Volume of Interest (VOI), which isπ×Rn²×tT) into other shapes for easy or meaningful computing purposes,for medical instrumentation purposes, or for clearer final datapresentation purposes. For example, the long cylinder of the biopsyspecific tissue (with radius Rn and height tT) may be transformed into aplanar cylinder (with radius Rw, which is the radius Rn multiplied bythe square root of the number of the MRI slices having the specifictissue to be biopsied extend therethrough) to match the MRI slicethickness T. The information of the radius Rw of the planner cylinder,which has a volume the same or about the same as the volume of thebiopsied specific tissue, i.e., VOI, and has a height of the MRI slicethickness T, is used to define the size (e.g., the radius) of a movingwindow in calculating a probability map for a patient (e.g., human). Theinvention proposes that, for each of the data sets, the volume of thebiopsy specific tissue, i.e., VOI, may be substantially equal to thevolume of the moving window to be used in calculating probability maps.In other words, the volume of the biopsy specific tissue, i.e., VOI,defines the size of the moving window to be used in calculatingprobability maps. The concept of obtaining a feature size (e.g., theradius) of the moving window to be used in calculating a probability mapfor an MRI slice is disclosed as above mentioned. Statistically, themoving window may be determined with the radius Rw (i.e., feature size),perpendicular to a thickness of the moving window, based on astatistical distribution or average of the radii Rw (calculated fromVOIs) associated with a subset data from the big data database. Next, aclassifier for an event such as biopsy-diagnosed tissue characteristicfor specific cancerous cells or occurrence of prostate cancer or breastcancer is created based on the subset data associated with the eventfrom the big data database. The subset data may be obtained from alldata associated with the given event. A classifier or biomarker librarycan be constructed or obtained using statistical methods, correlationmethods, big data methods, and/or learning and training methods.

After the big data database and the classifier are created orconstructed, an image of a patient, such as MRI slice image (i.e., amolecular image) or other suitable image, is obtained by a device orsystem such as MRI system. Furthermore, based on the feature size, e.g.,the radius Rw, of the moving window obtained from the subset data in thebig data database, the size of a computation pixel, which becomes thebasic unit of the probability map, is defined. If the moving window iscircular, the biggest square inscribed in the moving window is thendefined. Next, the biggest square is divided into n² small squares eachhaving a width Wsq, where n is an integer, such as 2, 3, 4, 5, 6, ormore than 6. The divided squares define the size and shape of thecomputation pixels in the probability map for the image of the patient.The moving window may move across the patient's image at a regular stepor interval of a fixed distance, e.g., substantially equal to the widthWsq of the computation pixels. A stop of the moving window overlaps theneighboring stop of the moving window. Alternatively, the biggest squaremay be divided into n rectangles each having a width Wrec and a lengthLrec, where n is an integer, such as 2, 3, 4, 5, 6, 7, 8, or more than8. The divided rectangles define the size and shape of the computationpixels in the probability map for the image of the patient. The movingwindow may move across the patient's image at a regular step or intervalof a fixed distance, e.g., substantially equal to the width of thecomputation pixels (i.e., the width Wrec), in the x direction and at aregular step or interval of a fixed distance, e.g., substantially equalto the length of computation pixels (i.e., the length Lrec), in the ydirection. A stop of the moving window overlaps the neighboring stop ofthe moving window. In an alternative embodiment, each of the stops ofthe moving window may have a width, length or diameter less than theside length (e.g., the width or length) of pixels, such as defined by aresolution of a MRI system, in the image of the patient.

After the size and shape of the computation pixel is obtained ordefined, the stepping of the moving window and the overlapping betweentwo neighboring stops of the moving window can then be determined.Measured values of specific imaging parameters for each stop of themoving window are obtained from the patient's molecular and/orstructural imaging information or image. The specific imaging parametersmay include molecular and/or structural imaging parameters, such as MRIparameters, PET parameters, SPECT parameters, micro-PET parameters,micro-SPECT parameters, Raman parameters, and/or BLO parameters, and/orother imaging parameters, such as CT parameters and/or ultrasoundimaging parameters. Each of the specific imaging parameters for eachstop of the moving window may have a value calculated based on anaverage of original measured values, for said each of the specificimaging parameters, for original pixels of the patient's image insidesaid each stop of the moving window. Some original pixels of thepatient's image may be only partially inside said each stop of themoving window. The average, for example, may be obtained from themeasured values, in said each stop of the moving window, each weighed byits area proportion of an area of the original pixel for said eachmeasured value to an area of said each stop of the moving window. Aregistered (multi-parametric) image dataset may be created for thepatient to include multiple imaging parameters, such as molecularparameters and/or other imaging parameters, obtained from variousequipment, machines, or devices, at a defined time-point (e.g., specificdate) or in a time range (e.g., within five days after treatment). Eachof the image parameters in the patient's registered (multi-parametric)image dataset requires alignment or registration. The registration canbe done by, for examples, using unique anatomical marks, structures,tissues, geometry, shapes or using mathematical algorithms and computerpattern recognition.

Next, the specific imaging parameters for each stop of the moving windowmay be reduced using, e.g., subset selection, aggregation, anddimensionality reduction into a parameter set for said each stop of themoving window. In other words, the parameter set includes measuredvalues for independent imaging parameters. The imaging parametersselected in the parameter set may have multiple types, such as twotypes, more than two types, more than three types, or more than fourtypes, (statistically) independent from each other or one another, ormay have a single type. For example, the imaging parameters selected inthe parameter set may include (a) MRI parameters and PET parameter, (b)MRI parameters and SPET parameters, (c) MRI parameters and CTparameters, (d) MRI parameters and ultrasound imaging parameters, (e)Raman imaging parameters and CT parameters, (f) Raman imaging parametersand ultrasound imaging parameters, (g) MRI parameters, PET parameters,and ultrasound imaging parameters, or (h) MRI parameters, PETparameters, and CT parameters.

Next, the parameter set for each stop of the moving window is matched tothe classifier to obtain a probability PW or CL_(m)

_(n) of the event for said each stop of the moving window. Thisinvention discloses an algorithm to compute a probability dl_(k)

_(l) of the event for each of the computation pixels P_(k)

_(l) from the probabilities PWs or CL_(m)

_(n) of the event for the stops W_(m)

_(n) of the moving window covering said each of the computation pixels,as described in the following steps ST1-ST11. In the step ST1, a firstor initial probability PV1 or dl_(k)

_(l) for each of the computation pixels P_(k)

_(l) is calculated or assumed based on an average of the probabilitiesPWs or CL_(m)

_(n) of the event for the stops W_(m)

_(n) of the moving window overlapping said each of the computationpixels P_(k)

_(l). In the step ST2, a first probability guess PG1 for each stop W_(m)

_(n) of the moving window is calculated by averaging the first orinitial probabilities PV1s or dl_(k)

_(l) (obtained in the step ST1) for all the computation pixels P_(k)

_(l) inside said each stop W_(m)

_(n) of the moving window. In the step ST3, the first probability guessPG1 for each stop of the moving window is compared with the probabilityPW of CL_(m)

_(n) of the event for said each stop W_(m)

_(n) of the moving window by subtracting the probability PW of CL_(m)

_(n) of the event from the first probability guess PG1 for said eachstop W_(m)

_(n) of the moving window so that a first difference DW1 (DW1=PG1−PW)between the first probability guess PG1 and the probability PW or CL_(m)

_(n) of the event for said each stop W_(m)

_(n) of the moving window is obtained. In the step ST4, a firstcomparison is performed to determine whether the absolute value of thefirst difference DW1 for each stop W_(m)

_(n) of the moving window is less than or equal to a preset thresholderror. If any one of the absolute values of all the first differencesDW1s is greater than the preset threshold error, the step ST5 continues.If the absolute values of all the first differences DW1s are less thanor equal to the preset threshold error, the step ST11 continues. In thestep ST5, a first error correction factor (ECF1) for each of thecomputation pixels P_(k)

_(l) is calculated by summing error correction contributions from thestops W_(m)

_(n) of the moving window overlapping said each of the computationpixels P_(k)

_(l). For example, if there are four stops W_(m)

_(n) to said one of the computation pixels P_(k)

_(l) is calculated by correction contribution from each of the fourstops W_(m)

_(n) to said one of the computation pixels P_(k)

_(l) is calculated by obtaining an area ratio of an overlapped areabetween said one of the computation pixels P_(k)

_(l) and said each of the four stops W_(m)

_(n) to an area of the biggest square inscribed in said each of the fourstops W_(m)

_(n), and then multiplying the first difference DW1 for said each of thefour stops W_(m)

_(n) by the area ratio. In the step ST6, a second probability PV2, i.e.,updated dl_(k)

_(l), for each of the computation pixels P_(k)

_(l) is calculated by subtracting the first error correction factor ECF1for said each of the computation pixels P_(k)

_(l) from the first or initial probability PV1 or dl_(k)

_(l) for said each of the computation pixels P_(k)

_(l) (PV2=PV1−ECF1). In the step ST7, a second probability guess PG2 foreach stop W_(m)

_(n) of the moving window is calculated by averaging the secondprobabilities PV2s, i.e., updated dl_(k)

_(l), (obtained in the step ST6) of all the computation pixels P_(k)

_(l) inside said each stop W_(m)

_(n) of the moving window. In the step ST8, the second probability guessPG2 for each stop W_(m)

_(n) of the moving window is compared with the probability PW or CL_(m)

_(n) of the event for said each stop W_(m)

_(n) of the moving window by subtracting the probability PW of CL_(m)

_(n) of the event from the second probability guess PG2 for said eachstop W_(m)

_(n) of the moving window so that a second difference DW2 (DW2=PG2−PW)between the second probability guess PG2 and the probability PW ofCL_(m)

_(n) of the event for said each stop W_(m)

_(n) of the moving window is obtained. In the step S9, a secondcomparison is performed to determine whether the absolute value of thesecond difference DW2 for each stop W_(m)

_(n) of the moving window is less than or equal the preset thresholderror. If any one of the absolute values or all the second differencesDW2s is greater than the preset threshold error, the step ST10continues. If the absolute values of all the second differences DW2s areless than or equal to the preset threshold error, the step ST11continues. In the step ST10, the steps ST5-ST9 are repeated or iterated,using the n^(th) difference DWn between the n^(th) probability guess PGnand the probability PW or CL_(m)

_(n) of the event for each stop W_(m)

_(n) of the moving window for calculation in the (n+1)^(th) iteration,until the absolute value of the (n+1)^(th) difference DW(n+1) for saideach stop W_(m)

_(n) of the moving window is equal to or less than the preset thresholderror (Note: PG1, PG1 and DW1 for the first iteration, ECF1, PV2, PG2and DW2 for the second iteration, and ECF(n−1). PVn, PGn and DWn for then^(th) iteration). In the step ST11, the first or initial probabilitiesPV1s in the first iteration, i.e., the steps ST1-ST4, the secondprobabilities PV2s in the second iteration, i.e., the steps ST5-ST9, orthe (n+1)^(th) probabilities PV(n+1)s in the (n+1)^(th) iteration, i.e.,the step ST10, are used to form the probability map. The probabilitiesdl_(k)

_(l) of the event for the computation pixels P_(k)

_(l) are obtained using the above method, procedure or algorithm, basedon overlapped stops W_(m)

_(n) of the moving window, to form the probability map of the event forthe image of the patient (e.g., patient's MRI slice) having imaginginformation (e.g., molecular and/or structural imaging information). Theabove process using the moving window in the x-y direction would createa two-dimensional (2D) probability map. In order to obtain athree-dimensional (3D) probability map, the above processes for all MRIslices of the patient would be performed in the z direction in additionto the x-y direction.

After the probability map is obtained, the patient may undergo a biopsyto obtain a tissue sample from an organ of the patient (i.e., that isshown on the image of the patient) at a suspected region of theprobability map. The tissue sample is then sent to be examined bypathology. Based on the pathology diagnosis of the tissue sample, it canbe determined whether the probabilities for the suspected region of theprobability map are precise or not. In the invention, the probabilitymap may provide information for a portion or all of the organ of thepatient with a spatial volume greater than 80% or even 90% of thespatial volume of the organ, than the spatial volume of the tissuesample (which may be less than 10% or even 1% of the spatial volume ofthe organ), and/or than the spatial volume of the specific tissueprovided for the first and second sets of information data in the bigdata database.

In order to further achieve the above objectives, the invention mayprovide a method of forming a probability-change map of theaforementioned event for a treatment. The method is described in thefollowing steps: (1) obtaining probabilities CL_(m)

_(n) of the event for respective stops W_(m)

_(n) of the moving window on pre-treatment and post-treatment images(e.g., MRI slice) of a patient in accordance with the methods andprocedures as described above, wherein the probability CL_(m)

_(n) of the event for each stop W_(m)

_(n) of the moving window on the pre-treatment image of the patient canbe obtained based on values C_(m)

_(n) for molecular and/or structural imaging parameters (and/or otherimaging parameters) taken before the treatment; similarly, theprobability CL_(m)

_(n) of the event for each stop W_(m)

_(n) of the moving window on the post-treatment image of the patient canbe obtained based on values C_(m)

_(n) for the molecular and/or structural imaging parameters (and/orother imaging parameters) taken after the treatment; all the valuesC_(m)

_(n) for the molecular and/or structural imaging parameters (or otherimaging parameters) taken before the treatment are obtained from theregistered (multi-parametric) image dataset for the pre-treatment image;all the values C_(m)

_(n) for the molecular and/or structural imaging parameters (or otherimaging parameters) taken after the treatment are obtained from theregistered (multi-parametric) image dataset for the post-treatmentimage; (2) calculating a probability change PMC or CCL_(m)

_(n) between the probabilities of the event before and after thetreatment for each stop W_(m)

_(n) of the moving window; and (3) calculating a probability change PVCor cdl_(k)

_(l) for each of computation pixels P_(k)

_(l) associated with the treatment based on the probability changes PMCsor CCL_(m)

_(n) for the stops W_(m)

_(n) of the moving window by following the methods and proceduresdescribed above for calculating the probability change PVC or cdl_(k)

_(l) of each or computation pixels P_(k)

_(l) from the probability changes PMCs or CCL_(m)

_(n) of the stops W_(m)

_(n) of the moving window based on the above algorithm to substitute theprobability changes PMCs or CCL_(m)

_(n) into the probabilities PMs or CL_(m)

_(n) for the stops W_(m)

_(n) of the moving window. The obtained probability changes PVCs orcdl_(k)-l for the computation pixels P_(k)

_(l) then compose a probability-change map of the event for thetreatment. Performing the above processes for all images (e.g., MRIslices) in the z direction, a 3D probability-change map of the event forthe treatment can be obtained.

In general, the invention proposes an objective to provide a method,system (including, e.g., hardware, devices, computers, processors,software, and/or tools), device, tool, software or hardware for formingor generating a decision data map, e.g., a probability map, based onfirst data of a first type (e.g., first measured values of MRIparameters) from a first subject such as a human or an animal. Themethod, system, device, tool, software or hardware may include buildinga database of big data (or call a big data database) including seconddata of the first type (e.g., second measured values of the MRIparameters) from a population of second subjects and third data of asecond type (e.g., biopsy results, data or information) from thepopulation of second subjects. The third data of the second type mayprovide information data with decisive, conclusive results for a betterjudgment or decision making (e.g., a patient whether to have a specificcancer or not). The second and third data of the first and second typesfrom each of the second subjects in the population, for example, may beobtained from a common portion of said each of the second subjects inthe population. A classifier related to a decision-making characteristic(e.g., occurrence of prostate cancer or breast cancer) is established orconstructed from the database of big data. The method, system, device,tool, software or hardware may provide a computing method including analgorithm for generating the decision data map with finer computationvoxels or pixels associated with the decision-making characteristic forthe first subject by matching the first data of the first type to theestablished or constructed classifier. The method, system, device, tool,software or hardware provides a decisive-and-conclusive-result-basedevidence for a better judgment or decision making based on the firstdata of the first type (without any data of the second type from thefirst subject). The second data of the first type, for example, may beobtained by a non-invasive method or a less-invasive method (as comparedto a method used to obtain the third data of the second type) or may beobtained more easily (as compared to the method used to obtain the thirddata of the second type). The second data of the first type may provideinformation, obtained by, e.g., a non-invasive method, for a specifictissue, to be biopsied or to be obtained by an invasive method, of anorgan of each second subject with a spatial volume covering, e.g., lessthan 10% or even less than 1% of the spatial volume of the organ of saideach second subject. The second data of the first type may includemeasured values or data of molecular imaging (and/or other imaging)parameters, such as measured values of MRI parameters and/or CT data.The third data of the second type, for example, may be obtained by aninvasive method or a more-invasive method (as compared to the methodused to obtain the second data of the first type) or may be harder toobtain (as compared to the method used to obtain the second data of thefirst type). The third data of the second type may provide informationfor the specific tissue, having been biopsied or obtained by an invasivemethod, of the organ of each second subject, third data of the secondtype may include biopsy results, data or information (for example apatient whether to have a cancer or not) for the biopsied specifictissues of the second subjects in the population. The decision makingmay be related to, for example, a decision on whether the first subjecthas cancerous cells or not. This invention provides a method to makebetter decision, judgment or conclusion for the first subject (apatient, for example) based on the first data of the first type, withoutany data of the second type from the first subject. This inventionprovides a method to use MRI imaging data to directly diagnose whetheran organ or tissue (such as breast or prostate) of the first subject hascancerous cells or not without performing a biopsy test for the firstsubject. In general, this invention provides a method to make decisiveconclusion, with 90% or over 90% of accuracy (or confidence level), orwith 95% or over 95% of accuracy (or confidence level), or eventually,with 99% or over 99% of accuracy (or confidence level). Furthermore, theinvention provides a probability map with its spatial resolution ofcomputation voxels or pixels that is 75%, 50% or 25%, in one dimension(1D), smaller than that of machine-defined original voxels or pixels ofan image created by the current available method. The machine-definedoriginal voxels or pixels of the image, for example, may be originalvoxels or pixels of an MRI image.

The present application presents a method for generating athree-dimensional computational map for a three-dimensional object. Themethod comprises: (1) applying a three-dimensional moving window to thethree-dimensional object to obtain a first value for each stop of thethree-dimensional moving window, wherein first and second ones of thestops are in a first plane and partially overlap with each other, andfirst and third ones of the stops are in a second plane and partiallyoverlap with each other, wherein the first and second planes arevertical to each other; and (2) calculating a second value for acomputation voxel of the three-dimensional computational map based oninformation associated with the first values for the first, second andthird ones of the stops each covering the computation voxel, wherein thecomputation voxel has a smaller volume than that of thethree-dimensional moving window.

In accordance with the method in the last paragraph, thethree-dimensional object may be constructed from multiple slices ofmedical images, e.g., magnetic-resonance-imaging (MRI) images, cut alongthe same direction for an organ tissue. A size of one of the computationvoxels of the three-dimensional computational map may be substantiallyequal to or smaller than that of one of multiple machine-definedoriginal voxels of the medical images. The first and second ones of thestops are neighboring two shifted from each other by a distancesubstantially equal to a first side length, in the first plane, of oneof the computation voxels, the first and third ones of the stops areneighboring two shifted from each other by a distance substantiallyequal to a second side length, in the second plane, of said one of thecomputation voxels, wherein the second side length is substantiallyvertical to the first side length. Said calculating the second valuesfor the respective computation voxels comprises calculating multipleassumed values for the respective computation voxels based oninformation associated with the first values for the stops covering therespective computation voxels. For more elaboration, said calculatingthe second value comprises: calculating an assumed value for thecomputation voxel based on information associated with the first valuesfor the stops each covering the computation voxel, calculating multipleguesses for the respective stops each covering the computation voxelbased on information associated with the assumed value for thecomputation voxel, calculating multiple differences each between one ofthe guesses and one of the first values for one of the stops of saidmoving window each covering the computation voxel, and updating theassumed value for the computation voxel based on information associatedwith the differences for the stops each covering the computation voxel.

The present application presents another method for generating athree-dimensional computational map for a three-dimensional object. Theanother method comprises: (1) applying a three-dimensional moving windowto the three-dimensional object to obtain multiple values for each stopof the three-dimensional moving window, wherein first and second ones ofthe stops are in a first plane and partially overlap with each other,and first and third ones of the stops are in a second plane andpartially overlap with each other, wherein the first and second planesare vertical to each other; (2) calculating a first probability or afirst event for said each stop based on information associated with thevalues for said each stop; and (3) calculating a second probability ofthe first event for a computation voxel of the three-dimensionalcomputational map based on information associated with the firstprobabilities for the first, second and third ones of the stops eachcovering the computation voxel, wherein the computation voxel has asmaller volume than that of the three-dimensional moving window.

In accordance with the another method in the last paragraph, saidcalculating the first probability of the first event for said each stopcomprises matching the values for said each stop to a classifier for thefirst event. The first event is associated with occurrence of a cancer.The three-dimensional object is constructed from multiple slices ofmedical images, e.g., magnetic-resonance-imaging (MRI) images, cut alongthe same direction for an organ tissue. A size of one of the computationvoxels of the three-dimensional computational map is substantially equalto or smaller than that of one of multiple machine-defined originalvoxels of the medical images. The first and second ones of the stops areneighboring two shifted from each other by a distance substantiallyequal to a first side length, in the first plane, of one of thecomputation voxels, the first and third ones of the stops areneighboring two shifted from each other by a distance substantiallyequal to a second side length, in the second plane, of said one of thecomputation voxels, wherein the second sidle length is substantiallyvertical to the first side length. The another method in the lastparagraph may further comprises calculating a third probability of asecond event for said each stop based on information associated with thevalues for said each stop, and calculating a fourth probability of thesecond event for the computation voxel of the three-dimensionalcomputational map based on information associated with the thirdprobabilities for the first, second and third ones of the stops. Thefirst event is associated with occurrence of a cancer, and the secondevent is associated with occurrence of a Gleason score or occurrence ofGleason scores in a range. Said calculating the second probabilitycomprises: calculating an assumed probability for the computation voxelbased on information associated with the first probabilities for thestops each covering the computation voxel, calculating multipleprobability guesses for the respective stops each covering thecomputation voxel based on information associated with the assumedprobability for the computation voxel, calculating multiple differenceseach between one of the probability guesses and one of the firstprobabilities for one of the stops of said moving window each coveringthe computation voxel, and updating the assumed probability for thecomputation voxel based on information associated with the differencesfor the stops each covering the computation voxel.

Another aspect of the disclosure provides a method of big-dataengineering learning based on data set (one or more parameters) of stopsof the 2D moving window, wherein the data set of the stops of the 2Dmoving window are obtained by a convolution method based on data set(one or more measured parameters, for example T1, T2, KTrans, tau orother MRI parameters) of original pixels of the 2D original map. Anengineering learning process is performed based on the data set of thestops of the moving window, for example based on Bayesian classifier, toobtain a learnt resulting parameter, for example a probability of canceroccurrence. The learnt resulting parameters of the computational pixelsof the 2D computational map are obtained by a deconvolution method basedon the learnt resulting parameters of the stops of the 2D moving window.The disclosure provides a method for better resolution of the 2Dcomputational map. As an example, the current MRI technology may providea resolution with a high confidence level (for example greater than 99%confidence level) at 3 mm; while a resolution with a low confidencelevel (for example less than 90% confidence level) at 1 mm. The originalpixel with a size of 1 mm-by-1 mm of the 2D original map may be used inthis disclosure. The disclosure may provide a method for improving theconfidence level from less than 90% to greater than 99% for the learntresulting parameters of the computational pixels with sizes of 1 mm-by-1mm of the 2D computational map. The disclosure may also provide a methodfor improving the resolution for the learnt resulting parameters of thecomputational pixels with sizes at 0.5 mm-by-0.3 mm of the 2Dcomputational map. The disclosure provides a method using a movingwindow in a standard size or in a few standard specific sizes to reducethe amount of the data or information of the original pixel of theoriginal map required in the big-data engineering learning, wherein thedata or information of the original pixel of the original map may beobtained by invasive methods for example obtained from biopsy samples.

Another aspect of the disclosure provides a method of big-dataengineering learning based on data set (one or more parameters) of stopsof the 3D moving window, wherein the data set of the stops of the 3Dmoving window are obtained by a convolution method based on data set(one or more measured parameters, for example T1, T2, KTrans, tau orother MRI parameters) of original voxels of the 3D original map. Anengineering learning process is performed based on the data set of thestops of the moving window, for example based on Bayesian classifier, toobtain a learnt resulting parameter, for example a probability of canceroccurrence. The learnt resulting parameters of the computational voxelsof the 3D computational map are obtained by a deconvolution method basedon the learnt resulting parameters of the stops of the 3D moving window.The disclosure provides a method for better resolution of the 3Dcomputational map. As an example, the current MRI technology may providea resolution with a high confidence level (for example greater than 99%confidence level) at 3 mm; while a resolution with a low confidencelevel (for example less than 90% confidence level) at 1 mm. The originalvoxel with a size of 1 mm-by-1 mm-1 mm of the 3D original map may beused in this disclosure. The disclosure may provide a method forimproving the confidence level from less than 90% to greater than 99%for the learnt resulting parameters of the computational voxels withsizes of 1 mm-by-1 mm-1 mm of the 3D computational map. The disclosuremay also provide a method for improving the resolution for the learntresulting parameters of the computational voxels with sizes at 0.5mm-by-0.5 mm of the 3D computational map. The disclosure provides amethod using a moving window in a standard size or in a few standardspecific sizes to reduce the amount of the data or information of theoriginal voxel of the original map required in the big-data engineeringlearning, wherein the data or information of the original voxel of theoriginal map may be obtained by invasive methods for example obtainedfrom biopsy samples.

Another aspect of the disclosure provides better resolution for a 2Ddata map based on a convolution method by obtaining data set (one ormore parameters) of stops of the 2D moving window based on data set (oneor more measured parameters, for example T1, T2, KTrans, tau or otherMRI parameters) of original pixels of the 2D original map. The data setsof the computational pixels of the 2D computational map are obtained bya deconvolution method based on the data sets of the stops of the 2Dmoving window. The disclosure provides a method for better resolution ofthe 2D computational map. As an example, the current MRI technology mayprovide a resolution with a high confidence level (for example greaterthan 99% confidence level) at 3 mm; while a resolution with a lowconfidence level (for example less than 90% confidence level) at 1 mm.The original pixel with a size of 1 mm-by-1 mm of the 2D original mapmay be used in this discloser. The disclosure may provide a method forimproving the confidence level from less than 90% to greater than 99%for the parameters of the computational pixels with sizes of 1 mm-by-1mm of the 2D computational map, with the same size of the original pixelof the original map. The disclosure may also provide a method forimproving the resolution for the parameters of the computational pixelswith sizes at 0.5 mm-by-0.5 mm of the 2D computational map.

Another aspect of the disclosure provides better resolution for a 3Ddata map based on a convolution method by obtaining data set (one ormore parameters) of stops of the 3D moving window based on data set (oneor more measured parameters, for example T1, T2, KTrans, tau or otherMRI parameters) of original pixels of the 3D original map. The data setsof the computational pixels of the 3D computational map are obtained bya deconvolution method based on the data sets of the stops of the 3Dmoving window. The disclosure provides a method for better resolution ofthe 3D computational map. As an example, the current MRI technology mayprovide a resolution with a high confidence level (for example greaterthan 99% confidence level) at 3 mm; while a resolution with a lowconfidence level (for example less than 90% confidence level) at 1 mm.The original voxel with a size of 1 mm-by-1 mm-by-1 mm of the 3Doriginal map may be used in this disclosure. This disclosure may providea method for improving the confidence level from less than 90% togreater than 99% for the parameters of the computational voxels withsizes of 1 mm-by-1 mm-by-1 mm of the 3D computational map, with the samesize of the original voxel of the original map. The disclosure may alsoprovide a method for improving the resolution for the parameters of thecomputational voxels with sizes at 0.5 mm-by-0.5 mm-by-0.5 mm of the 3Dcomputational map.

Another aspect of the disclosure provides a method for watching oridentifying a uniform region in the 2D computational map, wherein thelearnt resulting parameters for the computational pixels in the 2Dcomputational map are uniform (within a given spec).

(Another aspect of the disclosure provides a method for searching oridentifying a uniform space in the 3D computational map, wherein thelearnt resulting parameters for the computational voxels in the 3Dcomputational map are uniform (within a given spec).

Another aspect of the disclosure provides a method for searching oridentifying a uniform region in the 2D computational map, wherein thedata set for the computational pixels in the 2D computational map areuniform (within a given spec).

Another aspect of the disclosure provides a method for searching oridentifying a uniform region in the 3D computational map, wherein thedata set for the computational voxels in the 3D computational map areuniform (within a given spec).

Another aspect of the disclosure provides measured data sets of stops ofthe moving window by the overlapping sampling method.

These, as well as other components, steps, features, benefits, andadvantages of the present disclosure, will now become clear from areview of the following detailed description or illustrativeembodiments, the accompanying drawings, and the claims.

BRIEF DESCRIPTION OF THE DRAWINGS

The drawings disclose illustrative embodiments of the presentdisclosure. They do not set forth all embodiments. Other embodiments maybe used in addition or instead. Details that may be apparent orunnecessary may be omitted to save space or for more effectiveillustration. Conversely, some embodiments may be practiced without allof the details that are disclosed. When the same reference number orreference indicator appears in different drawings, it may refer to thesame or like components or steps.

Aspects of the disclosure may be more fully understood from thefollowing description when read together with the accompanying drawings,which are to be regarded as illustrative in nature, and not as limiting.The drawings are not necessarily to scale, emphasis instead being placedon the principles of the disclosure. In the drawings:

FIG. 1A is a schematic drawing showing a “Big Data” probability mapcreation in accordance with an embodiment of the present invention.

FIGS. 1B-1G show a subset data table in accordance with an embodiment ofthe present invention, wherein data in the subset data table weregenerated by using published data and applying some individual personalexperience and judgement. The data are used as a demonstration example;

FIGS. 1H-1M show a subset data table in accordance with an embodiment ofthe present invention;

FIG. 2A is a schematic drawing showing a biopsy tissue and multiple MRIslices registered to the biopsy tissue in accordance with an embodimentof the present invention;

FIG. 2B is a schematic drawing of a MRI slice in accordance with anembodiment of the present invention;

FIG. 2C is a schematic drawing showing multiple machine-defined originalpixels of a MRI slice covered by a region of interest (ROI) on the MRIslice in accordance with an embodiment of the present invention;

FIG. 2D shows a data table in accordance with an embodiment of thepresent invention;

FIG. 2E shows a planar cylinder transformed from a long cylinder of abiopsied tissue in accordance with an embodiment of the presentinvention;

FIG. 3A is a schematic drawing showing a circular window and atwo-by-two grid array within a square inscribed in the circular windowin accordance with an embodiment of the present invention;

FIG. 3B is a schematic drawing showing a circular window and athree-by-three grid array within a square inscribed in the circularwindow in accordance with an embodiment of the present invention;

FIG. 3C is a schematic drawing showing a circular window and afour-by-four grid array within a square inscribed in the circular windowin accordance with an embodiment of the present invention;

FIG. 4 is a flow chart illustrating a computing method of generating orforming a probability map in accordance with an embodiment of thepresent invention;

FIG. 5 shows a MRI slice showing a prostate, as well as a computationregion on the MRI slice, in accordance with an embodiment of the presentinvention;

FIG. 6A is a schematic drawing showing a circular window moving, acrossa computation region of a MRI slice in accordance with an embodiment ofthe present invention;

FIG. 6B shows a square inscribed in a circular window having a corneraligned with a corner of a computation region of a MRI slice inaccordance with an embodiment of the present invention;

FIG. 7A is a schematic drawing showing multiple machine-defined originalpixels of a MRI slice covered by a circular window in accordance with anembodiment of the present invention;

FIG. 7B shows a data table in accordance with an embodiment of thepresent invention;

FIG. 8 is a flow chart depicting an algorithm for generating aprobability map in accordance with an embodiment of the presentinvention;

FIG. 9 shows a computation region defined with thirty-six computationvoxels for a probability map in accordance with an embodiment of thepresent invention;

FIGS. 10A, 10C, 10E, 10G, 11A, 11C, 11E, 11G, 12A, 12C, 12E, 12G, 13A,13C, 13E, and 13G show sixteen stops of a circular moving window, eachof which includes nine non-overlapped small squares, in accordance withan embodiment of the present invention;

FIGS. 10B, 10D, 10F, 10H, 11B, 11D, 11F, 11H, 12B, 12D, 12F, 12H, 13B,13D, 13F, and 13H show a circular window moving across a computationregion defined with thirty-six computation voxels in accordance with anembodiment of the present invention;

FIGS. 14A, 14B, and 14C show initial probabilities for computationvoxels, updated probabilities for the computation voxels, and optimalprobabilities for the computation voxels, respectively, in accordancewith an embodiment of the present invention;

FIGS. 15A-15C show three probability maps;

FIG. 15D shows a composite probability image or map;

FIG. 16 shows a MRI slice showing a breast, as well as a computationregion on the MRI slice, in accordance with an embodiment of the presentinvention;

FIGS. 17A-17R show a description or various parameters (“parametercharts” and “biomarker” charts could be used to explain many items thatcould be included in a big data database, this would include theontologies, mRNA, next generation sequencing, etc., and exact data in“subset” databases could then be more specific and more easily generateddata);

FIG. 18 is a flow chart depicting a method of evaluating, identifying,or determining the effect of a treatment (e.g., neoadjuvant chemotherapyor minimally invasive treatment of prostate cancer) or a drug used inthe treatment on a subject in accordance with an embodiment of thepresent invention;

FIG. 19 is a flow chart depicting a method of evaluating, identifying,or determining the effect of a treatment or a drug used in the treatmenton a subject in accordance with an embodiment of the present invention;

FIG. 20 is a flow chart depicting a method of evaluating, identifying,or determining the effect of a treatment or a drug used in the treatmenton a subject in accordance with an embodiment of the present invention;

FIG. 21 is a diagram showing two Gaussian curves of two given differentgroups with respect to parameter measures;

FIG. 22A illustrates a process of using an E operator to obtain betterresolution of probabilities of an event in a two-dimensional region inaccordance with an embodiment of the present application;

FIG. 22B illustrates another process of using an E operator to obtainbetter resolution of probabilities of an event in a two-dimensionalregion in accordance with an embodiment of the present application;

FIG. 23A illustrates a process of using an E operator to obtain betterresolution of measured values in a two-dimensional region in accordancewith an embodiment of the present application

FIG. 23B illustrates another process of using an E operator to obtainbetter resolution of measured values in a two-dimensional region inaccordance with an embodiment of the present application.

FIG. 24 illustrates a schematic view showing a three-dimensional (3D)image of a three-dimensional object in accordance with the presentapplication.

FIG. 25 illustrates a schematic view showing a three-dimensional (3D)moving window in accordance with an embodiment of the presentapplication

FIGS. 26A-26C are schematic views showing a process of applying athree-dimensional moving window to a three-dimensional image to obtainbetter resolution in the 3D image in accordance with an embodiment ofthe present application

FIGS. 26D-26J are schematically views showing two of the stops of a 3Dmoving window partially overlapping with each other in various manners.

FIG. 27A illustrates a process of using an E operator to obtain betterresolution of measured values in a two-dimensional region orthree-dimensional space in accordance with an embodiment of the presentapplication.

FIG. 27B illustrates a process of using an E operator to obtain betterresolution of values for pixels or voxels of a two-dimensional orthree-dimensional map in accordance with another embodiment of thepresent application

FIG. 28A illustrates a process of using an E operator to obtain betterresolution of probabilities of an event in a two-dimensional region orthree-dimensional space in accordance with an embodiment of the presentapplication

FIG. 28B illustrates another process of using an E operator to obtainbetter resolution of probabilities of an event in a two-dimensionalregion in accordance with an embodiment of the present application.

FIG. 29A illustrates a schematic view showing a moving window for movingacross target and outside regions in accordance with an embodiment ofthe present application

FIGS. 29B-29D are schematic views showing moving windows at rightmostand bottommost corner of a two-dimensional computational map inaccordance with an embodiment of the present application.

FIGS. 30A and 30B illustrate schematic views showing a moving window formoving across target and outside spaces of a three-dimensional originalmap in accordance with an embodiment of the present application

FIG. 31A illustrates a process of using an E operator to obtain betterresolution of measured values in a two-dimensional region orthree-dimensional space in accordance with an embodiment of the presentapplication.

FIG. 31B illustrates a process of using an E operator to obtain betterresolution of values for pixels or voxels of a two-dimensional orthree-dimensional map in accordance with another embodiment of thepresent application.

FIG. 32A illustrates a process of using an E operator to obtain betterresolution of probabilities of an event for pixels or voxels of atwo-dimensional or three-dimensional probability map in accordance withan embodiment of the present application.

FIG. 32B illustrates a process or using an E operator to obtain betterresolution of probabilities of an event for pixels or voxels of atwo-dimensional or three-dimensional probability map in accordance withanother embodiment of the present application.

FIG. 33A illustrates a schematic view showing a uniform regiondetermined in a two-dimensional region in accordance with an embodimentof the present application.

FIG. 33B illustrates a schematic view showing a uniform space determinedin a three-dimensional computational map in accordance with anembodiment of the present application.

FIGS. 33C and 33D illustrate various schematic views showing a stop of athree-dimensional moving window, not overlapping a uniform space,partially overlap with another stop of the three-dimensional movingwindow partially overlapping the uniform in accordance with anembodiment of the present application.

FIGS. 34A-34H are schematically view showing various situations of eachstop W_((m)

₁₎

_((n)

₁₎-W_((m)

₁₎

_((n)

₁₎, W_((m)

₁₎

_(n), W_((m)

₁₎

_(n), W_((m)

₁₎

_((n)

₁₎-W_((m)

₁₎

_((n)

₁₎ of the moving window partially overlapping a specific stop W_(m)

_(n) of the moving window.

FIG. 35A is a schematic view showing a two-dimensional moving windowprovided with four measuring pixels arranged in a 2-by-2 array inaccordance with an example of the present application.

FIG. 35B is a schematic view showing a measuring pixel of atwo-dimensional moving window has a profile defined by a profile of acombination of nine computation pixels, arranged in a 3-by-3 array, of atwo-dimensional computational map in accordance with an example of thepresent application.

FIGS. 35C-35K are schematic views showing a path of a two-dimensionalmoving windows in accordance with the present application.

While certain embodiments are depleted in the drawings, one skilled inthe art will appreciate that the embodiments depicted are illustrativeand that variations of those shown, as well as other embodimentsdescribed herein, may be envisioned and practiced within the scope ofthe present disclosure.

DETAILED DESCRIPTION OF THE INVENTION

Illustrative embodiments are now described. Other embodiments may beused in addition or instead. Details that may be apparent or unnecessarymay be omitted to save space or for a more effective presentation.Conversely, some embodiments may be practiced without all of the detailsthat are disclosed.

First Aspect: E Operator for Better Resolution of Probabilities of Eventin Two-Dimensional Region via Big-Data Engineering Learning I-1.Probability Map Derived from Measured Values for Original Pixels ofTwo-Dimensional Original Map

FIG. 22A illustrates a process of using an E operator to obtain betterresolution of probabilities of an event in a two-dimensional region inaccordance with an embodiment of the present application. Referring toFIGS. 5, 6A and 22A, in a step S22-1 for convolution operation (E_(c)),a two-dimensional moving window 2 is applied to one or a plurality oftwo-dimensional original maps registered to or aligned with each otheror one another, wherein the one or each of the plurality oftwo-dimensional original maps is provided with multiple originalmeasured values of a specific one of one or more imaging parameters,such as parameter of T1, T2, Ktrans or tau for an MRI parameter orparameter obtained from an optical image captured by a camera, each forone of its original pixels P_(i)

_(j) arranged in a two-dimensional array, wherein the one or each of theplurality of two-dimensional original maps is registered to andassociated with and covers a target region 11 for a biologicalstructure, to obtain one or a set of values C_(m)

_(n) of the one or more imaging parameters, such as parameters of T1, T2and Ktrans for MRI parameters, parameters of T1, T2 and tau for MRIparameters or parameters obtained from one or more optical imagescaptured by one or more cameras, for each stop W_(m)

_(n) of the two-dimensional moving window 2. In this case, the originalmeasured values for the respective original pixels p_(i)

_(j) of the one or each of the plurality of two-dimensional originalmaps may be associated with an MRI parameter, the one or each of theplurality of two-dimensional original maps may be associated with an MRIslice or a combination of multiple MRI slices registered to or alignedwith the target region 11. The one or each of the set of values C_(m)

_(n) of a specific one of the one or more imaging parameters for saideach stop W_(m)

_(n) of the two-dimensional moving window 2 is calculated or obtainedbased on one or more of the original measured values of the specific oneof the one or more imaging parameters for respective one or more of theoriginal pixels p_(i)

_(j) of the one or one of the plurality of two-dimensional originalmaps, which are covered by or associated with said each stop W_(m)

_(n) of the two-dimensional moving window 2. Said each stop W_(m)

_(n) of the two-dimensional moving window 2 has a larger area than thatof each of the respective one or more of the original pixels p_(i)

_(j) of the one or each of the plurality of two-dimensional originalmaps. Each neighboring two of the stops W_(m)

_(n) n in a x direction may partially overlap with each other with ashift equal to a x-direction width X_(fp) of computation pixels P_(k)

_(l) of a two-dimensional computational map 12. Each neighboring two ofthe stops W_(m)

_(n) in a y direction may partially overlap with each other with a shiftequal to a y-direction width Y_(fp) of the computation pixels P_(k)

_(l) of the two-dimensional computational map 12.

Next, in a step S22-2 for big-data engineering learning, a learntresulting parameter, i.e., a probability CL_(m)

_(n) of an event, for each stop W_(m)

_(n) is calculated or obtained by matching the one or the set of valuesC_(m)

_(n) of the one or more imaging parameters for said each stop W_(m)

_(n) of the two-dimensional moving window 2 to a classifier such asBayesian classifier. The probability CL_(m)

_(n) of the event for each stop W_(m)

_(n) of the two-dimensional moving window 2 is independent of an area ofsaid each stop W_(m)

_(n).

Next, in a step S22-3 for deconvolution operation (E_(d)), a probabilitydl_(k)

_(l) of the event for each computation pixel P_(k)

_(l) of the two-dimensional computational map 12 is iteratively updatedor calculated, as illustrated in steps ST1-ST11 in following paragraphsin the first aspect, based on one or more of the probabilities CL_(m)

_(n) of the event for respective one or more of the stops W_(m)

_(n) each covering said each computation pixel P_(k)

_(l), wherein said each computation pixel P_(k)

_(l) has a smaller area than that of each of the respective one or moreof the stops W_(m)

_(n) of the two-dimensional moving window 2. The probability dl_(k)

_(l) of the event for each computational pixel P_(k)

_(l) is independent of an area of said each computational pixel P_(k)

_(l).

One aspect of the disclosure provides an algorithm, a method, or anoperator, for transformation of data, dataset or information related tooriginal or initial pixels (p_(i)

_(j)) at respective locations, x_(i)

_(j)'s of a 2D region to a new data, dataset or information in a finalor computation pixels (P_(k)

_(l)) at related locations X_(k)

_(l)'s, of the same 2D region, wherein i, j, k, l are positive integers,i from 1, 2, . . . , to l; j from 1, 2, . . . , to J; k from 1, 2, . . ., to K; l from l1, 2, . . . , to L. The transformation results in a newset of data, dataset or information of the final or computation pixelswith a better resolution and a lower noise as compared to that of theoriginal or initial pixels. K may be different from I and L may bedifferent from J. For a better resolution and a lower noise, the area ofeach of the final or computation pixels is smaller than that of theoriginal or initial pixels; that is K>L and I>J. Alternatively, when I=Kand J=L, X_(k)

_(l) can be the same as x_(i)

_(j), wherein the noises due to measurement fluctuation in the data,dataset or information of the original or initial pixels aresmeared-out. The 2D region may comprise I×J pixels in grids of originalor initial pixels, wherein the size and numbers of pixels may bedetermined by a certain detector or sensor used in obtaining the data,dataset or information related to the original or initial pixels. The 2Dregion may as well comprise K×L pixels in grids of final or computationpixels, wherein the size and numbers of pixels may be generated for adesired resolution for analysis, diagnosis or a specific application.The data, dataset or information related to the original or initialpixels may be of a certain type, property, category or item (forexample, MRI parameters) obtained from a certain detector or sensor. Thedata, dataset or information related to the final or computation pixelsmay be of a same type, property, category or item (as that, for examplethe MRI parameters, of the original or initial pixels) obtained from thetransformation or computation. Alternatively, the data, dataset orinformation related to the original or initial pixels may be, forexamples, the IR absorption images for a given range of wavenumbers, theRaman scattering images for a given range of wavenumbers, thefluorescent light images for a given range of wavenumbers, or theultrasonic images of a human organ. The original or initial pixels havea dimension in one direction (for example, x direction) x_(op), and adimension in the perpendicular direction (for example, y direction)y_(op), while the final pixels have a dimension in one direction (forexample, x direction) X_(fp), and a dimension in the perpendiculardirection (for example, y direction) Y_(fp). The final pixels may havethe same dimensions (size) as that of the original pixels, or with eachpixel having a size larger or smaller than the size of original orinitial pixels, while both are in the same 2D region. The data, datasetor information in or related to, or describing each of the original orinitial pixels (p_(i)

_(j)) can be a number, multiple numbers, a real number, multiple realnumbers, a digitized number (for example a negative integer, 0, or apositive integer), multiple digitized numbers, a 0 or 1, multiple 0's or1's, a scalar, multiple scalars, a vector, multiple vectors, or a tensorwith degree of order 0, 1, 2, . . ., t, where t is an integer.

The disclosed algorithm or operator comprises two operations, aconvolution operation (E_(c)) and the deconvolution operation (E_(d)).E_(c) and E_(d) can be operated separately or together. When combiningthese two operations together, it is the Engineering operator (Eoperator). E=E_(d)E_(c). The operator, as well as the E_(c) and E_(d)operators will be described and specifies as follows.

The original data, dataset or information in the original or initialpixels in a given 2D region is transformed to a data, dataset orinformation in stops of a moving window, with the data, dataset orinformation of the same type, property, category or item (for example,MRI parameters) as that (for example, a MRI parameters) of the originaldata, dataset or information in the original or initial pixels. Themoving window plays a key role in the E operator or E algorithm. It isdefined with some physical, computation, analytical, or statisticalpurposes for better resolution and lower noise. The size, shape,parameters or format of the moving window may become a default orstandard size, shape, parameters or format in collecting, storing,computing, (statistically) analyzing data or information, or engineeringlearning or machine learning. Usually, the size, shape, parameters orformat of the moving window is chosen to enclose at least severaloriginal or initial pixels, as well as at least several final orcomputation pixels. For example, the moving window size and shape can bedefined in a 2D MRI slice with a total volume (moving window area timesthe thickness or height of the MRI slice) is equal to a volume of abiopsy sample, wherein the volume of a biopsy sample may be defined bythe averaged volume of biopsy samples taken in the standard biopsyprocedure using needles with popular or standard sizes. The movingwindow area mentioned above is defined as the size, shape, parameters orformat of the moving window in the 2D region. The moving window may havea shape of a circle, an elliptic, a square or a rectangle. When themoving widow has a shape of circle, the maximum inscribed square maycontain p×p original or initial pixels; or P×P final or computationpixels: wherein p and P are positive numbers, and is greater than orequal to 1. P, in some cases, is chosen to be a positive integer, and isgreater than or equal to 2. When the moving widow has a shape ofelliptic, the maximum inscribed rectangle may contain p×q original orinitial pixels; or P×Q final or computation pixels: where p q, P and Qare positive numbers, and are greater than or equal to 1. P and Q, insome cases, are chosen to be positive integers, and are greater than orequal to 2. When the moving widow has a shape or square, the square maycontain p×p original or initial pixels, or P×P final or computationpixels; where p, and P are positive numbers, and are greater than orequal to 1.P, in some cases, is chosen to be a positive integer, and isgreater than or equal to 2. When the moving widow has a shape ofrectangle, the rectangle may contain p×q original or initial pixels; orP×Q final or computation pixels; where p, q, P and Q are positivenumbers, and greater than or equal to 1. P and Q, in some cases, arechosen to be positive integers, and are greater than or equal to 2. Themoving widow are stepping in the same 2D region by a step of X_(fp) inthe x direction and a step of Y_(fp) in the y direction, and resultingin an array of densely populated and overlapped stops. Each stopoverlaps its nearest neighbor stop with a step or shift of X_(fp) orY_(fp), in the x and y directions, respectively. Each stop in the 2Dregion comprises a number of original pixels, full or partial. The data,dataset or information for each stop is obtained by averaging over allthe pixels enclosed by the stop. For some partially enclosed pixels, theaveraging computation over these pixels can be done by weighing theenclosed area proportionally. The averaging can be done by linearaveraging, Gaussian averaging or Lorentian averaging. In linearaveraging, we assume the data, dataset or information in each stop ofmoving window is uniform. The above method transforms data, dataset orinformation in the original or initial pixels to data, dataset orinformation in stops of moving window, wherein the transform can becalled a convolution. The stop of moving window at location X_(m)

_(n) is defined as W_(m)

_(n), wherein m=1, 2, 3, 4, . . . , M, and n=1, 2, 3, 4, . . . N. Thedata, dataset or information in or related to each stop of the movingwindow (W_(m)

_(n)) can be a number, multiple numbers, a real number, multiple realnumbers, a digitized number (for example a negative integer, 0, or apositive integer), multiple digitized numbers, a 0 or 1, multiple 0's or1's, a scalar, multiple scalars, a vector, multiple vectors, or a tensorwith degree of order 0, 1, 2, . . . , t, wherein t is an integer. Sincethe moving window is stepping by the size of a final or computationpixel, the number of the stops is counted in the array of final orcomputation pixels. Assuming each stop of moving comprises P×Qcomputation pixels. The original matrix M_(op) comprises I×J pixels andhas I×J sets or elements or components of data, dataset or information.The convolution matrix M_(cw) comprises (K−P+1)×(L−Q+1) stops of movingwindow, and has (K−P+1)×(L−Q+1) sets or elements or components of data,dataset or information. The E_(c) operator transforms original matrixM_(op) (comprising I×J sets or elements of data, dataset or information(for example, MRI parameters) describing or representing each originalpixel in the given 2D region) to a convolution matrix M_(cw) (comprising(K−P+1)×(L−Q+1) sets or elements of averaged data, dataset orinformation (for example, MRI parameters) describing or representingeach stop of moving window in the given 2D region) can be expressed as:

E _(c)(M _(op) , W _(PQ))=M _(cw)

Wherein M_(op) has dimension or size I×J, the moving window W_(PQ) hasdimension or size P×Q, and M_(cw) has dimension or size (K−P+1)×(L−Q+1).The M_(cw) comprise elements of data, dataset, or information of thesame type, properly, category or item as that of M_(op). For example,the elements in both M_(cw) and M_(op) are data, dataset or informationrelated to the MRI parameters. Alternatively, the elements in bothM_(cw) and M_(op) are data, dataset or information related to the IRabsorption, Raman scattering, fluorescent light, or ultrasonic imaging.

In this aspect, engineering learning or machine learning is performedusing the data, dataset or information related to the moving window, orusing the standard size, shape, parameters or format or dimensions ofthe moving window. The description and specification of the steps,processes and methods related to the convolution operator are the sameas in the above. As described and specified above, the convolutionoperator E_(c) transforms the original matrix M_(op) (comprising data,dataset or information (for example, MRI parameters) describing orrepresenting each original or initial pixel in the given 2D region) to aconvolution matrix M_(cw) (comprising averaged data, dataset orinformation (for example, MRI parameters) describing or representingeach stop of moving window in the given 2D region). Through theengineering learning, machine learning or correlation, the data, datasetor information of the elements of M_(cw) may be transformed to a data,dataset or information in a different type, property, item or category.For example, based on big data (accumulated data of correlated clinicalbiopsy analysis data and the measured MRI parameters for patients) andusing (for example) Bayesian inference, the M_(op) (elements of MRIparameters) can be transformed or constructed into a matrix of learningwindow ML_(w) comprising elements of the probabilities of canceroccurrence. Since the 2D moving window is stepping by the size of afinal or computation pixel, the number of the stops is counted in a 2Darray of final or computation pixels. Each stop of 2D moving windowcomprises P×Q final or computation pixels. The original matrix M_(op)comprises I×J pixels and has I×J sets or elements or components of data,dataset or information. The convolution matrix M_(cw) and the learningmatrix ML_(w) both comprise (K−P+1)×(L−Q+1) stops of 2D moving window,and has (K−P+1)×(L−Q+1) sets or elements or components of data, datasetor information. The E_(c) operator transforms original matrix M_(op)(comprising I×J sets or elements of data, dataset or information (forexample, MRI parameters) describing or representing each original pixelin the given 2D region) to a convolution matrix (comprising(K−P+1)×(L−Q+1) sets or elements of averaged data, dataset orinformation (for example, MRI parameters) describing or representingeach stop of 2D moving window in the given 2D region). The E_(l)operator transforms the convolution matrix M_(cw) (comprising(K−P+1)×(L−Q+1) sets or elements of averaged data, dataset orinformation (for example, MRI parameters) describing or representingeach stop of 2D moving window in the given 2D region) to a learningmatrix ML_(w) (comprising (K−P+1)×(L−Q+1) sets or elements of averageddata, dataset or information (for example, the probability of the canceroccurrence) describing or representing each stop of 2D moving window inthe given 2D region). The engineering learning operator (or the machinelearning operator), E_(l), can be expressed as:

E _(l)(M _(cw) , W _(PQ))=ML _(w)

wherein the 2D moving window comprises P×Q final or computation pixelswith P and Q in the x and y directions, respectively, and the stopsW_(m)

_(n)'s are at locations with m and n final or computation pixels in thegiven 2D region, wherein m=1, 2, 3, . . . , M, and n=1, 2, 3, . . . , N.The data, dataset or information in or related to, or describing eachelement of the learning matrix ML_(w) for the stop W_(m)

_(n) in the given 2D region is of a different type, properly, categoryor item (for example, the probability of the occurrence of a cancer) ascompared to that (for example, MRI parameters) in or related to, ordescribing each element of the convolution matrix M_(cw) for the stopW_(m)

_(n) in the same given 2D region. While the data, dataset or informationin or related to, or describing each element of the convolution matrixM_(cw) for the stop W_(m)

_(n) in the given 2D region is of a same type, property, category oritem (for example, MRI parameters) as compared to that (for example, MRIparameters) in or related to, or describing each element of the originalmatrix M_(op) for the original or initial pixel in the same given 2Dregion. Alternatively, the data, dataset or information related to theoriginal or initial pixels may be, for examples, the IR absorptionimages for a given range of wavenumbers, the Raman scattering images fora given range of wavenumbers, the fluorescent light images for a givenrange of wavenumbers, or the ultrasonic images of human organ. Asdescribed and specified in the above, the moving window plays a key rolein the engineering learning operator or algorithm (E operator). It isdefined with some physical, computation, analytical, or statisticalpurposes. Furthermore, the size, shape, parameters or format of themoving window is used for the engineering learning or machine learning.The size, shape, parameters or format of the moving window may become adefault or standard size or format in collecting, storing, computing,(statistically) analyzing data or information, or engineering learningor machine learning. The methods, algorithms or procedures ofengineering learning or machine learning for transforming M_(cw) toML_(w) may be, for example, using (i) statistics, for example, Bayesianinference, (ii) connection or association, for example, neuro-computing,(iii) Symbolism: for example, induction or interpretation, (iv) analog,for example, resemblance, (v) evolution, for example, nature processes.

Similar to the deconvolution of M_(cw) described and specified above,the learning matrix ML_(w) can be also deconvoluted to obtain a final orcomputational matrix ML_(dp). The size, shape, parameters or format ofthe final or computation pixels are described and specified as in theabove. The deconvolution matrix ML_(dp) comprises a final orcomputational data, dataset or information for each final or computationpixel in the given 2D region. The data, dataset or information in orrelated to, or describing each pixel P_(k)

_(l) of the final or computation pixels in the given 2D region are ofthe same type, property, category or item (for example, the probabilityof the occurrence of a cancer) as that (for example, the probability ofthe occurrence of a cancer) of the learned data, dataset or informationof the elements in ML_(w) for the stops W_(m)

_(n) of moving window. The data, dataset or information in or relatedto, or describing each pixel P_(k)

_(l) of the final or computation pixels in the given 2D region are of adifferent type, property, category or item (for example, the probabilityof the occurrence of a cancer) as that (for example, MRI parameters) ofthe data, dataset or information of the elements in M_(cw) for the stopsW_(m)

_(n) of moving window. The data, dataset or information in or relatedto, or describing each pixel P_(k)

_(l) of the final or computation pixels in the given 2D region are of adifferent type, property, category or item (for example, the probabilityof the occurrence of a cancer) as that (for example, MRI parameters) ofthe data, dataset or information of the elements in M_(op) for theoriginal or initial pixels x_(i)

_(j). Alternatively, for examples, based on big data (accumulated dataof correlated clinical biopsy analysis result or data and the measuredIR absorption, Raman scattering data, fluorescent lights, or ultrasonicimaging from the correspondent biopsy samples of patients) and using,for example, Bayesian inference, the M_(op) (IR absorption, Ramanscattering data, fluorescent light intensity, or ultrasonic imaging) canbe transformed or constructed into a matrix of learning window ML_(w)comprising elements of the probabilities of cancer occurrence.

The data, dataset or information in or related to, or describing eachpixel P_(k)

_(l) of the final or computation pixels can be a number, multiplenumbers, a real number, multiple real numbers, a digitized number (forexample a negative integer, 0, or a positive integer), multipledigitized numbers, a 0 or 1, multiple 0's or 1's, a scalar, multiplescalars, a vector, multiple vectors, or a tensor with degree of order 0,1, 2, . . . , t, where t is an integer. The deconvolution E_(d) of the Eoperator obtains the data, dataset or information for each final orcomputation pixel by solving a set of linear equations with unknowncomputation pixel data (dl_(k)

_(l)'s) and known data (CL_(m)

_(n)'s) of stops of the moving windows. The linear equations can beestablished by equating the data, dataset or information for each movingwindow stop W_(m)

_(n) to the data, dataset or information averaged over all the final orcomputation pixels enclosed by the moving window stop (W_(m)

_(n)), dl_(k)

_(l). The averaging can be done by linear averaging, Gaussian averagingor Lorentian averaging dl_(k)

_(l)'s.

$\begin{matrix}{\mspace{79mu} {{{\frac{1}{P*Q}\text{?}\text{?}} = {CL}_{m - n}}{\text{?}\text{indicates text missing or illegible when filed}}}} & (6)\end{matrix}$

Wherein dl_(k)

_(l)'s are the data, dataset or information of the final or computationpixels enclosed or within by the stop of the moving window W_(m)

_(n), wherein k is from k₁ to k₁+P−1, and l is from l₁ to l₁+Q−1, andm=1, 2, 3, . . . , K−P+1, and n=1, 2, 3, . . . , L−Q+1.

There are (K−P+1)×(L−Q+1) equations with knows (CL_(m)

_(n)'s) and K×L unknowns (dl_(k)

_(l)'s). The number of unknown is larger than the number of equations(6) by (PL+KQ−PQ−K−L+P+Q−1). A method to increase number of knows anddecrease number of unknowns will be described below by (1) findinguniform or constant data, dataset or information for the final orcomputation pixels in a region or regions of uniformity or approximatelyuniformity within the 2D region of interest, and/or (2) finding uniformor constant data, dataset or information for the final or computationpixels in a region or regions of uniformity or approximately uniformityextending from and near or along the boundary of the 2D region ofinterest. The above method (1) may provide a number of knows (known datafor the computation pixels) equal to or larger than the number of(PL+KQ−PQ−K−L+P+Q−1) such that the number (K−P+1)×(L−Q+1) of theequations (6) may be solved. If the moving window comprises 3-by-3computation pixels, the above method (2) may provide a number of knows(known data for the computation pixels) equal to or larger than thenumber of [(K+2)(L+2)−(K−P+3)×(L−Q+3)] such that the number(K−P+3)×(L−Q+3) of the equations (6) may be solved. The set of linearequations can be solved by a computer, device, machine, processor,system or tool iteratively. The initial guess of each of the unknowns(the data, dataset or information of final or computation pixels),dl_(k)

, is obtained by averaging over all the stops of covering or enclosingthe pixel. The contribution from each enclosing stop calculated by thearea ratio of the overlapped area (A′_(m)

_(n)) to the area of that stop (A_(m)

_(n)). dl_(k)

can be obtained using A_(m)

_(n), A′_(m)

_(n) and CL_(m)

_(n).

$\begin{matrix}{\mspace{79mu} {{\text{?} = {\sum_{m_{1},n_{1}}^{m_{2},m_{2}}{\frac{\text{?}}{A_{m - n}}{CL}_{m - n}}}}{\text{?}\text{indicates text missing or illegible when filed}}}} & (2)\end{matrix}$

Wherein stops W_(m)

_(n) cover or enclose the final or computation pixel P_(k)

_(l) has stop indices m from m₁ to m₂, and n from n₁ to n₂. In the firstiteration, we can calculate and obtain the first data, dataset orinformation for each stop of the moving window, CL_(m)

_(n1)'s, by using initial guess dl_(k)

's in equation (2). The iteration results in a solution ML_(dp)(K×L)when the set of computation pixel data or information match the set oflearning window data or information with errors or difference smallerthan or equal to a specified value or number in the same 2D region. TheE_(d) operator can be expressed as:

E _(d)(ML _(w) , W _(PQ))=ML _(dp)

In another aspect of the disclosure, the convolution operator E_(c), thelearning operator E_(l) and the deconvolution operator E_(d) can beperformed in sequence to get the full E operator. The E operatortransform the original matrix M_(op) (comprising elements of data,dataset or information for the I×J original or initial pixels and hasI×J sets or elements or components of data or information) to thedeconvolution matrix M_(dp) (comprising elements of data, dataset orinformation for the K×L pixels and has K×L sets or elements orcomponents of data or information) in the same given 2D region, throughthe convolution window matrix M_(cw) (comprising (K−P+1)×(L−Q+1) sets orelements or components of data or information of the convolution windowstops) and through the learning window matrix ML_(w) (comprising(K−P+1)×(L−Q+1) sets or elements or components of data or information ofthe learning window stops). The E operator can be expressed as

E(M _(op)(I×J))=E _(d)(ML _(w)((K−P+1)×(L−Q+1)))=E _(d) E _(l)(M_(cw)((K−P+1)×(L−Q+1)))=E _(d) E _(l) E _(c)(M _(op)(I×J))=ML _(dp)(K×L)

In another aspect of the disclosure, this invention discloses the Eoperator in the linear algebra. The linear operations, such as addition(+), subtraction (−), multiplication by a scalar (d) or division by ascalar (l), are performed using the data or information of each stop ofthe moving window, (that is using the elements in the convolution matrixM_(cw) or the elements in the learning matrix ML_(w)), instead of usingthe data or information of the original or initial pixels (that isinstead of using the elements in the convolution matrix M_(op).) Themoving window is used as a default or standard size, configuration orformat for containing and providing data, dataset or information foranalysis, comparison, computing, engineering learning or machinelearning.

E(a Σ _(s) C _(s) M _(s))=M

Where M_(s) or M is a matrix of the convolution matrix M_(cw), or thelearning matrix ML_(w), and C_(s) are the real numbers, s is an integerfrom 1, 2, 3, . . . , S, with S a positive integer.

A method described in the first aspect is performed using MRI detectionand diagnosis as an example. The algorithm in the first aspect may beemployed to transform, via the engineering learning E, the value setsC_(m)

_(n), each having the values for various MRI parameters, for therespective stops W_(m)

_(n) of the 2D moving window into the computation pixel data dl_(k)

_(l), i.e., probabilities of an event, for the respective computationpixels P_(k)

_(l).

Alternatively, each combination of computed tomography (CT) parameters,position emission tomography (PET) parameters, single-photon emissioncomputed tomography (SPECT) parameters, micro-PET parameters,micro-SPECT parameters, Raman parameters, and/or bioluminescence optical(BLO) parameters, ultrasound parameters, infrared absorbance parameters,camera-image parameters and/or visible-light-image parameters may alsobe taken for a value set C_(m)

_(n) for one of the stops W_(m)

_(n) of the 2D moving window in the first aspect. The data, dataset orinformation C_(m)

_(n) for the stops W_(m)

_(n) of the 2D moving window in the first aspect may be obtained fromdetection or analysis instruments, such as camera, microscope (opticalor electronic), endoscope, detectors or spectrometer (visible light,fluorescent light, IR, UV or X-ray), ultrasonic machine or system,magnetic resonance imaging (MRI) machine or system, computed tomography(CT) machine or system, position emission tomography (PET) machine orsystem, single-photon emission computed tomography (SPECT) machine orsystem, micro-PET machine or system, micro-SPECT machine or system,Raman spectrometer or system, and/or bioluminescence optical (BLO)machine or system, or other machine for obtaining molecular orstructural imaging data.

For further elaboration, an example for MRI detection is mentioned asbelow:

Computing methods described in the present invention may be performed onany type of image, such as molecular and structural image (e.g., MRIimage, CT image, PET image, SPECT image, micro-PET, micro-SPECT, Ramanimage, or bioluminescence optical (BLO) image), structural image (e.g.,CT image or ultrasound image), fluoroscopy image, structure/tissueimage, optical image, infrared image, X-ray image, or any combination ofthese types of images, based on a registered (multi-parametric) imagedataset for the image. The registered (multi-parametric) image datasetmay include multiple imaging data or parameters obtained from one ormore modalities, such as MRI, PET, SPECT, CT, fluoroscopy, ultrasoundimaging, BLO imaging, micro-PET, micro-SPECT, Raman imaging,structure/tissue imaging, optical imaging, infrared imaging, and/orX-ray imaging. For a patient, the registered (multi-parametric) imagedataset may be created by aligning or registering in space allparameters obtained from different times or from various machines.Methods in first, second and third embodiments of the invention may beperformed on a MRI image based on the registered (multi-parametric)image dataset, including, e.g., MRI parameters and/or PET parameters,for the MRI image.

Referring to FIG. 1A, a big data database 70 is created to includemultiple data sets, each of which may include: (1) a first set ofinformation data, which may be obtained by a non-invasive method or aless-invasive method (as compared to a method used to obtain thefollowing second set of information data), wherein the first set of datainformation may include measured values for multiple imaging parameters,including, e.g., molecular and structural imaging parameters (such asMRI parameters, CT parameters, PET parameters, SPECT parameters,micro-PET parameters, micro-SPECT parameters, Raman parameters, and/orBLO parameters) and/or other structural imaging data (such as from CTand/or ultrasound images), for a volume and location of a tissue to bebiopsied (e.g., prostate or breast) from a subject such as human oranimal, (2) combinations each of specific some of the imagingparameters, (3) dimensions related to imaging parameters (e.g.,molecular and structural imaging parameters), such as the thickness T ofan MRI slice and the size of an MRI original pixel of the MRI slice,including the width or side length of the MRI original pixel and thethickness or height of the MRI original pixel (which may besubstantially equal to the thickness of the MRI slice), (4) a second setof information data obtained by an invasive method or a more-invasivemethod (as compared to the method used to obtain the first set ofinformation data), wherein the second set of the information data mayinclude tissue-based information from a biopsy performed on the subject,(5) clinical data (e.g., age and sex of the subject and/or Gleason scoreof a prostate cancer) associated with the biopsied tissue and/or thesubject, and (6) risk factors for cancer associated with the subject.

Some or all of the subjects for creating the big data database 70 mayhave been subjected to a treatment such as neoadjuvant chemotherapy or(preoperative) radiation therapy. Alternatively, some or all of thesubjects for creating the big data database 70 are not subjected to atreatment such as neoadjuvant chemotherapy or (preoperative) radiationtherapy. The imaging parameters in each of the data sets of the big datadatabase 70 may be obtained from different modalities, including two ormore of the following, MRI, PET, SPECT, CT, fluoroscopy, ultrasoundimaging, BLO imaging, micro-PET, micro-SPECT, and Raman imaging.Accordingly, the imaging parameters in each of the data sets of the bigdata database 70 may include four or more types of MRI parametersdepicted in FIGS. 17A-17H, one or more types of PET parameters depictedin FIG. 17I, one or more types of heterogeneity features depicted inFIG. 17J, and other parameters depicted in FIG. 17K. Alternatively, thefirst set of information data may only include a type of imagingparameter (such as T1 mapping). In each of the data sets of the big datadatabase 70, each of the imaging parameters (such as T1 mapping) for thetissue to be biopsied may have a value calculated based on an average ofmeasured values, for said each of the imaging parameters, for multipleregions, portions, locations or volumes of interest of multipleregistered images (such as MRI slices) registered to or aligned withrespective regions, portions, locations or volumes of the tissue to bebiopsied, wherein all of the regions, portions, locations or volumes ofinterest of the registered images may have a total volume covering andsubstantially equaling the volume of the tissue to be biopsied. Thenumber of the registered images for the tissue to be biopsied may begreater than or equal to 2, 5 or 10.

In the case of the biopsied tissue obtained by a needle, the biopsiedtissue may be long cylinder-shaped with a radius Rn, which issubstantially equal in an inner radius of the needle, and a height tTnormalized to the thickness T of the MRI slice. In the invention, thevolume of the long cylinder-shaped biopsied tissue may be transformedinto another shape, which may have a volume the same or about the sameas the volume of the long cylinder-shaped biopsied tissue (or Volume ofInterest, VOI, which may be π×Rn²×tT), for easy or meaningful computingpurposes, for medical instrumentation purposes, or for clearer finaldata presentation purposes. For example, the long cylinder of thebiopsied tissue with the radius Rn and height tT may be transformed intoa planar cylinder to match the MRI slice thickness T. The planarcylinder, for example, may have a height equal to the MRI slicethickness T, a radius Rw equal to the radius Rn multiplied by the squareroot of the number of the registered images, and a volume the same orabout the same as the volume of the biopsied tissue, i.e., VOI. Theradius Rw of the planner cylinder is used to define the size (e.g., theradius Rm) of a moving window MW in calculating a probability map for apatient (e.g., human). In the invention, the volume of the biopsiedtissue, i.e,. VOI, for each of the data sets, for example, may besubstantially equal to the volume of the moving window MW to be used incalculating probability maps. In other words, the volume of the biopsiedtissue, i.e., VOI, defines the size of the moving window MW to be usedin calculating probability maps. Statistically, the moving window MW maybe determined with the radius Rm, perpendicular to a thickness of themoving window MW, based on the statistical distribution or average ofthe radii Rw (calculated from multiple VOIs) associated with a subsetdata (e.g., the following subset data DB-1 or DB-2) from the big datadatabase 70.

The tissue-based information in each of the data sets of the big datadatabase 70 may include (1) a biopsy result, data, information (i.e.,pathologist diagnosis, example cancer or no cancer) for the biopsiedtissue, (2) mRNA data or expression patterns, (3) DNA data or mutationpatterns (including that obtained from next generation sequencing), (4)ontologies, (5) biopsy related feature size or volume (including theradius Rn of the biopsied tissue, the volume of the biopsied tissue(i.e., VOI), and/or the height tT of the biopsied tissue), and (6) otherhistological and biomarker findings such as necrosis, apoptosis,percentage of cancer, increased hypoxia, vascular reorganization, andreceptor expression levels such as estrogen, progesterone, HER2, andEPGR receptors. For example, regarding the tissue-based information ofthe big data database 70, each of the data sets may include specificlong chain mRNA biomarkers from next generation sequencing that arepredictive of metastasis-free survival, such as HOTAIR, RP11-2781.15.2-001, LINC00511-009, AC004231.2-001. The clinical data in each athe data sets of the big data database 70 may include the timing oftreatment, demographic data (e.g., age, sex, race, weight, family type,and residence of the subject), and TNM staging depicted in, e.g., FIGS.17N and 17O or FIGS. 17P, 17Q and 17R. Each of the data sets of the bigdata database 70 may further include information regarding neoadjuvantchemotherapy and/or information regarding (preoperative) radiationtherapy. Imaging protocol details, such as MRI magnet strength, pulsesequence parameters, PET dosing, time at PET imaging, may also beincluded in the big data database 70. The information regarding(preoperative) radiation therapy may include the type of radiation, thestrength of radiation, the total dose of radiation, the number offractions (depending on the type of cancer being treated), the durationof the fraction from start to finish, the dose of the fraction, theduration of the preoperative radiation therapy from start to finish, andthe type of machine used for the preoperative radiation therapy. Theinformation regarding neoadjuvant chemotherapy may include the givendrug(s), the number of cycles (i.e., the duration of the neoadjuvantchemotherapy from start to finish), the duration of the cycle from startto finish, and the frequency of the cycle.

Data of interest are selected from the big data database 70 into asubset, used to build a classifier CF. The subset from the big datadatabase 70 may be selected for a specific application, such as prostatecancer, breast cancer, breast cancer after neoadjuvant chemotherapy, orprostate cancer after radiation. In the case of the subset selected forprostate cancer, the subset may include data in a tissue-based orbiopsy-based subset data DB-1. In the ease of the subset selected forbreast cancer, the subset may include data in a tissue-based orbiopsy-based subset data DB-2. Using suitable methods, such asstatistical methods, correlation methods, big data methods, and/orlearning and training methods, the classifier CF may be constructed orcreated based on a first group associated with a first data type orfeature (e.g., prostate cancer or breast cancer) in the subset, a secondgroup associated with a second data type or feature (e.g., non-prostatecancer or non-breast cancer) in the subset, and some or all of thevariables in the subset associated with the first and second groups.Accordingly, the classifier CF for an event, such as the first data typeor feature, may be created based on the subset associated with the eventfrom the big data database 70. The event may be a biopsy-diagnosedtissue characteristic, such as having specific cancerous cells, oroccurrence of prostate cancer or breast cancer.

After the database 70 and the classifier CF are created or constructed,a probability map, composed of multiple computation pixels with the samesize, is generated or constructed for, e.g., evaluating or determiningthe health status of a patient (e.g., human subject), the physicalcondition of an organ or other structure inside the patient's body, orthe patient's progress and therapeutic effectiveness by the stepsdescribed below. First, an image of the patient is obtained by a deviceor system, such as MRI system. The image of the patient, for example,may be a molecular image (e.g., MRI image, PET image, SPECT image,micro-PET image, micro-SPECT image, Raman image, or BLO image) or othersuitable image (e.g., CT image or ultrasound image). In addition, basedon the radius Rm of the moving window MW obtained from the subset, e.g.,the subset data DB-1 or DB-2, in the big data database 70, the size ofthe computation pixel, which becomes the basic unit of the probabilitymap, is defined.

If the moving window MW is circular, the biggest square inscribed in themoving window MW is then defined. Next, the biggest square inscribed inthe moving window MW is divided into n² small squares i.e., cubes, eachhaving a width Wsq, where n is an integer, such as 2, 3, 4, 5, 6, ormore than 6. The divided squares define the size and shape of thecomputation pixels in the probability map for the image of the patient.For example, each of the computation pixels of the probability map maybe defined as a square, i.e., cube, having the width Wsq and a volumethe same or about the same as that of each of the divided squares. Themoving window MW may move across the image of the patient at a regularstep or interval of a fixed distance, e.g., substantially equal to thewidth Wsq (i.e., the width of the computation pixels), in the x and ydirections. A stop of the moving window MW overlaps the neighboring stopof the moving window MW.

Alternatively, the biggest square inscribed in the moving window MW maybe divided into n rectangles each having a width Wrec and a length Lrec,where n is an integer, such as 2, 3, 4, 5, 6, 7, 8, or more than 8. Thedivided rectangles define the size and shape of the computation pixelsin the probability map for the image of the patient. Each of thecomputation pixels of the probability map, for example, may be arectangle having the width Wrec, the length Lrec, and a volume the sameor about the same as that of each of the divided rectangles. The movingwindow MW may move across the patient's molecular image at a regularstep or interval of a fixed distance, e.g., substantially equal to thewidth Wrec (i.e., the width of the computation pixels), in the xdirection and at a regular step or interval of a fixed distance, e.g.,substantially equal to the length Lrec (i.e., the length of thecomputation pixels), in the y direction. A stop of the moving window MWoverlaps the neighboring stop of the moving window MW. In an alternativeembodiment, each of the stops of the moving window MW may have a width,length or diameter less than the side length (e.g., the width or length)of the machine-defined original pixels in the image of the patient.

After the size and shape of the computation pixels are obtained ordefined, the stepping of the moving window MW and the overlappingbetween two neighboring stops of the moving window MW can then bedetermined. Multiple values of specific imaging parameters for each stopof the moving window MW may be obtained from the patient's image and/ordifferent parameter maps (e.g., MRI parameter map(s), PET parametermap(s) and/or CT parameter map(s)) registered to the patient's image.The specific imaging parameters may include two or more of the followingMRI parameters, PET parameters, SPECT parameters, micro-PET parameters,micro-SPECT parameters, Raman parameters, BLO parameters, CT parameters,and ultrasound imaging parameters. Each of the specific imagingparameters for each stop of the moving window MW, for example, may havea value calculated based on an average of measured values, for said eachof the specific imaging parameters, for machine-defined original pixelsof the patient's image inside said each stop of the moving window MW. Inthe case that some machine-defined original pixels of the patient'simage only partially inside that stop of the moving window MW, theaverage can be weighed by the area proportion. The specific imagingparameters of different modalities may be obtained from registered imagesets (or registered value sets or parameter maps), and rigid andnon-rigid standard registration techniques may be used to get eachsection of anatomy into the same exact coordinate location on each ofthe registered (multi-parametric) image dataset.

A registered (multi-parametric) image dataset may be created for thepatient to include multiple registered images (including two or more ofthe following: MRI slice images, PET images, SPECT images, micro-PETimages, micro-SPECT images, Raman images, BLO images, CT images, andultrasound images) and/or corresponding imaging parameters (includingtwo or more of the following: MRI parameters, PET parameters, SPECTparameters, micro-PET parameters, micro-SPECT parameters, Ramanparameters, BLO parameters, CT parameters, and/or ultrasound imagingparameters) obtained from various equipment, machines, or devices orfrom a defined time-point (e.g., specific date) or time range (e.g.,within five days after treatment). Each of the imaging parameters in thepatient's registered (multi-parametric) image dataset requires alignmentor registration. The registration can be done by, for examples, usingunique anatomical marks, structures, tissues, geometry, and/or shapes orusing mathematical algorithms and computer pattern recognition. Thevalues of the specific imaging parameters for each stop of the movingwindow MW, for example, may be obtained from the registered(multi-parametric) image dataset for the patient.

Next, the specific imaging parameters for each stop of the moving windowMW may be reduced using, e.g., subset selection, aggregation, anddimensionality reduction into a parameter set for said each stop of themoving window MW. In other words, the parameter set includes values forindependent imaging parameters. The imaging parameters used in theparameter set may have multiple types, such as two types, more than twotypes, more than three types, or more than four types, independent fromeach other or one another, or may have a single type. For example, theimaging parameters used in the parameter see may include (a) MRIparameters and PET parameters, (b) MRI parameters and SPET parameters,(c) MRI parameters and CT parameters, (d) MRI parameters and ultrasoundimaging parameters, (e) Raman imaging parameters and CT parameters, (f)Raman imaging parameters and ultrasound imaging parameters, (g) MRIparameters, PET parameters, and ultrasound imaging parameters, or (h)MRI parameters, PET parameters, and CT parameters.

Next, the parameter set for each stop of the moving window MW is matchedto the classifier CF to obtain a probability PW or CL_(m)

_(n) of the event for said each stop of the moving window MW. After theprobabilities PWs or CL_(m)

_(n) of the event for the stops of the moving window MW are obtained, analgorithm is performed based on the probabilities PWs or CL_(m)

_(n) of the event for the stops of the moving window MW to computeprobabilities of the event for the computation pixels, as mentioned inthe following steps ST1-ST11. In the step ST1, a first or initialprobability PV1 for each of the computation pixels, for example, may becalculated or assumed based on an average of the probabilities PWs orCL_(m)

_(n) of the event for the stops of the moving window MW overlapping orcovering said each of the computation pixels. In the step ST2, a firstprobability guess PG1 for each stop of the moving window MW iscalculated by averaging the first or initial probabilities PV1s(obtained in the step ST1) of all the computation pixels inside saideach stop of the moving widow MW. In the step ST3, the first probabilityguess PG1 for each stop of the moving window MW is compared with theprobability PW or CL_(m)

_(n) of the event for said each stop of the moving window MW by, e.g.,subtracting the probability PW or CL_(m)

_(n) of the event from the first probability guess PG1 so that a firstdifference DW1 (DW1=PG1−PW) between the first probability guess PG1 andthe probability PW or CL_(m)

_(n) of the event for said each stop of the moving window MW isobtained. In the step ST4, a first comparison is performed to determinewhether an absolute value of the first difference DW1 for each stop ofthe moving window MW is less than or equal to a preset threshold error.If any one of the absolute values of all the first differences DW1s isgreater than the preset threshold error, the step ST5 continues. If theabsolute values of all the first differences DW1s are less than or equalto the preset threshold error, the step ST11 continues. In the step ST5,a first error correction factor (ECF1) for each of the computationpixels is calculated by, e.g., summing error correction contributionsfrom the stops of the moving window MW overlapping or covering said eachof the computation pixels. For example, if there are four stops of themoving window MW overlapping or covering one of the computation pixels,each of the error correction contributions to said one of thecomputation pixels is calculated by obtaining an area ratio of anoverlapped area between said one of the computation pixels and acorresponding one of the four stops to an area of the biggest squareinscribed in the corresponding one of the four stops, and thenmultiplying the first difference DW1 for the corresponding one of thefour stops by the area ratio. In the step ST6, a second probability PV2for each of the computation pixels is calculated by subtracting thefirst error correction factor ECF1 for said each of the computationpixels from the first or initial probability PV1 for said each of thecomputation pixels (PV2=PV1−ECF1). In the step ST7, a second probabilityguess PG2 for each stop of the moving window MW is calculated byaveraging the second probabilities PV2s (obtained in the step ST6) ofall the computation pixels inside said each stop of the moving widow MW.In the step ST8, the second probability guess PG2 for each stop of themoving window MW is compared with the probability PW or CL_(m)

_(n) of the event for said each stop of the moving window MW by, e.g.,subtracting the probability PW or CL_(m)

_(n) of the event from the second probability guess PG2 so that a seconddifference DW2 (DW2=PG2−PW) between the second probability guess PG2 andthe probability PW or CL_(m)

_(n) of the event for said each stop of the moving window MW isobtained. In the step S9, a second comparison is performed to determinewhether an absolute value of the second difference DW2 for each stop ofthe moving window MW is less than in equal the preset threshold error.If any one of the absolute values of all the second differences DW2s isgreater than the preset threshold error, the step ST10 continues. If theabsolute values of all the second differences DW2s are less than orequal to the preset threshold error, the step ST11 continues. In thestep ST10, the steps ST5-ST9 are repeated or iterated, using the newlyobtained the n^(th) difference DWn between the n^(th) probability guessPGn and the probability PW or CL_(m)

_(n) of the event for each stop of the moving window MW for calculationin the (n+1)^(th) iteration, until an absolute value of the (n+1)^(th)difference DW(n+1) for each stop of the moving window MW is equal to orless than the preset threshold error (Note: PV1, PG1 and DW1 for thefirst iteration, ECF1, PV2, PG2 and DW2 for the second iteration, andECF(n−1), PVn, PGn and DWn for the n^(th) iteration). In the step ST11,the first or initial probabilities PV1s in the first iteration, i.e.,the steps ST1-ST4, the second probabilities PV2s in the seconditeration, i.e., the steps ST5-ST9, or the (n+1)^(th) probabilitiesPV(n+1)s in the (n+1)^(th) iteration, i.e., the step ST10 are used toform the probability map. The probabilities of the event for thecomputation pixels are obtained using the above method, procedure oralgorithm, based on the overlapped stops of the moving window MW, toform the probability map of the event for the image (e.g., patient's MRIslice) for the patient having imaging information (e.g., molecularimaging information). The above process is performed to generate themoving window MW across the image in the x and y directions to create atwo-dimensional (2D) probability map. In order to obtain athree-dimensional (3D) probability map, the above process may be appliedto each of all images of the patient in the z direction perpendicular tothe x and y directions.

Description of Subset Data DB-1

Referring to FIGS. 1B-1G, the tissue-based or biopsy-based subset dataDB-1 from the big data database 70 includes multiple data sets eachlisted in the corresponding one of its rows 2 through N, wherein thenumber of the data sets may be greater than 100, 1,000 or 10,000.Each ofthe data sets in the subset data DB-1 may include: (1) measured valuesfor MRI parameters associated with a prostate biopsy tissue (i.e.,biopsied sample of the prostate) obtained from a subject (e.g., human),as shown columns A-O; (2) measured values for processed parametersassociated with the prostate biopsy tissue, as shown in columns P and Q;(3) a result or pathologist diagnosis of the prostate biopsy tissue,such as prostate cancer, normal tissue, or benign condition, as shown ina column R; (4) sample characters associated with the prostate biopsytissue, as shown in columns S-X; (5) MRI characters associated with MRIslices registered to respective regions, portions, locations or volumesof the prostate biopsy tissue, as shown in columns Y, Z and AA; (6)clinical or pathology parameters associated with the prostate biopsytissue or the subject, as shown in columns AB-AN; and (7) personalinformation associated with the subject, as shown in columns AO-AR.Needles used to obtain the prostate biopsy tissues may have the samecross-sectional shape (e.g., round shape or square shape) and the sameinner diameter or width, e.g., ranging from, equal to or greater than0.1 millimeters up to, equal to or less than 5 millimeters, and morepreferably ranging from, equal to or greater than 1 millimeter up to,equal to or less than 3 millimeters.

The MRI parameters in the columns A-O of the subset data DB-1 are T1mapping, T2 raw signal, T2 mapping, delta Ktrans (ΔKtrans), tau, DtIVIM, fp IVIM, ADC (high b-values), nADC (high b-values), R*, Ktransfrom Tofts Model (TM), Ktrans from Extended Tofts Model (ETM), Ktransfrom Shutterspeed Model (SSM), Ve from TM, and Ve from SSM. For moreinformation about the MRI parameters in the subset data DB-1, pleaserefer to FIGS. 17A through 17H. The processed parameter in the column Pof the subset data DB-1 is average Ve, obtained by averaging Ve from EMand Ve from SSM. The processed parameter in the column Q of the subsetdata DB-1 is average Ktrans, obtained by averaging Ktrans from TM,Ktrans from ETM, and Ktrans from SSM. All data can have normalizedvalues, such as z scores.

Measured values in the respective columns T, U and V of the subset dataDB-1 are Gleason scores associated with the respective prostate biopsytissues and primary and secondary Gleason grades associated with theGleason scores, FIG. 17L briefly explains Gleason score, the primaryGleason grade, and the secondary Gleason grade. Measured values in thecolumn W of the subset data DB-1 may be the diameters of the prostatebiopsy tissues, and the diameter of each of the prostate biopsy tissuesmay be substantially equal to an inner diameter of a cylinder needle,through which a circular or round hole passes for receiving said each ofthe prostate biopsy tissues. Alternatively, measured values in thecolumn W of the subset data DB-1 may be the widths of the prostatebiopsy tissues, and the width of each of the prostate biopsy tissues maybe substantially equal to an inner width of a needle, through which asquare or rectangular hole passes for receiving said each of theprostate biopsy tissues. The clinical or pathology parameters in thecolumns AB-AN of the subset data DB-1 are prostate specific antigen(PSA), PSA velocity, % free PSA, Histology subtype, location within agiven anatomical structure of gland, tumor size, PRADS, pathologicaldiagnosis (e.g., Atypia, benign prostatic hypertrophy (BPH), prostaticintraepithelial neoplasia (PIN), or Atrophy), pimonidazole immunoscore(hypoxia marker), pimonidazole genescore (hypoxia marker), primary tumor(T), regional lymph nodes (N), and distant metastasis (M). For moreinformation about the clinical or pathology parameters in the subsetdata DB-1, please refer to FIGS. 17M through 17O. Other data orinformation in the big data database 70 may be added to the subset dataDB-1. For example, each of the data sets in the subset data DB-1 mayfurther include risk factors for cancer associated with the subject,such as smoking history, sun exposure, premalignant lesions, geneinformation or data, etc. Each of the data sets in the subset data DB-1may also include imaging protocol details, such as MRI magnet strength,and pulse sequence parameters, and/or information regarding(preoperative) radiation therapy, including the type of radiation, thestrength of radiation, the total dose of radiation, the number offractions (depending on the type of cancer being treated), the durationof the fraction from start to finish, the dose of the fraction, theduration of the preoperative radiation therapy from start to finish, andthe type of machine used for the preoperative radiation therapy. Apost-therapy data or information for prostate cancer may also beincluded in the subset data DB-1. For example, data regarding ablativeminimally invasive techniques or radiation treatments (care for earlyprostate cancer or post surgery), imaging data or information followingtreatment, and biopsy results following treatment are included in thesubset data DB-1.

Referring to FIGS. 1D and 1E, data in the column W of the subset dataDB-1 are various diameters; data in the column X of the subset data DB-1are various lengths, data in the column Y of the subset data DB-1 arethe various numbers of MRI slices registered to respective regions,portions, locations or volumes of a prostate biopsy tissue, data in thecolumn Z of the subset data DB-1 are various MRI area resolutions; datain the column AA of the subset data DB-1 are various MRI slicethicknesses. Alternatively, the diameters of all the prostate biopsytissues in the column W of the subset data DB-1 may be the same; thelengths of all the prostate biopsy tissues in the column X of the subsetdata DB-1 may be the same; all the data in the column Y of the subsetdata DB-1 may be the same; all the data in the column Z of the subsetdata DB-1 may be the same; all the data in the column AA of the subsetdata DB-1 may be the same.

Description of Subset Data DB-2

Referring to FIGS. 1H-1M, the tissue-based or biopsy-based subset dataDB-2 from the big data database 70 includes multiple data sets eachlisted in the corresponding one of its rows 2 through N, wherein thenumber of the data sets may be greater than 100, 1,000 or 10,000. Eachof the data sets in the subset data DB-2 may include: (1) measuredvalues for MRI parameters associated with a breast biopsy tissue (i.e.,biopsied sample of the breast) obtained from a subject (e.g., human oranimal model), as shown in columns A-O, R, and S; (2) values forprocessed parameters associated with the breast biopsy tissue, as shownin columns P and Q; (3) features of breast tumors associated with thebreast biopsy tissue, as shown in columns T-Z; (4) a result orpathologist diagnosis of the breast biopsy tissue, such as breastcancer, normal tissue, or benign condition, as shown in a column AA; (5)sample characters associated with the breast biopsy tissue, as shown incolumns AB-AD; (6) MRI characters associated with MRI slices registeredto respective regions, portions, locations or volumes of the breastbiopsy tissue, as shown in columns AE-AG, (7) a PET parameter (e.g.,maximum standardized uptake value (SUVmax) depicted in FIG. 17I)associated with the breast biopsy tissue or the subject, as shown in acolumn AH, (8) clinical or pathology parameters associated with thebreast biopsy tissue or the subject, as shown columns AI-AT; and (9)personal information associated with the subject, as shown in columnsAU-AX. Needles used to obtain the breast biopsy tissues may have thesame cross-sectional shape (e.g., round shape or square shape) and thesame inner diameter or width, e.g., ranging from, equal to or greaterthan 0.1 millimeters up to, equal to or less than 5 millimeters, andmore preferably ranging from, equal to or greater than 1 millimeter upto, equal to or less than 3 millimeters. Alternatively, anintra-operative incisional biopsy tissue sampling may be performed by asurgery to obtain the breast biopsy. Intraoperative magnetic resonanceimaging (iMRI) may be used for obtaining a specific localization of thebreast biopsy tissue to be biopsied during the surgery.

The MRI parameters in the columns A-O, R, and S of the subset data DB-2are T1 mapping, T2 raw signal, T2 mapping, delta Ktrans (ΔKtrans), tau,Dt IVIM, fp IVIM, ADC (high b-values), R*, Ktrans from Tofts Model (TM),Ktrans from Extended Tofts Model (ETM), Khans from Shutterspeed Model(SSM), Ve from TM, Ve from SSM, kep from Tofts Model (TM), kep fromShutterspeed Model (SSM), and mean diffusivity (MD) from diffusiontensor imaging (DTI). For more information about the MRI parameters inthe subset data DB-2, please refer to FIGS. 17A through 17H. Theprocessed parameter in the column P of the subset data DB-2 is averageVe, obtained by averaging Ve from TM and Ve from SSM. The processedparameter in the column Q of the subset data DB-2 is average Ktrans,obtained by averaging Ktrans from TM, Ktrans from ETM, and Ktrans fromSSM. The features of breast tumors may be extracted from breast tumorswith dynamic contrast-enhanced (DCE) MR image.

Multiple values in the column AC of the subset data DB-2 may be thediameters of the breast biopsy tissues, and the diameter of each of thebreast biopsy tissues may be substantially equal to an inner diameter ofa cylinder needle, through which a circular or round hole passes forreceiving said each of the breast biopsy tissues. Alternatively, thevalues in the column AC of the subset data DB-2 may be the widths of thebreast biopsy tissues, and the width of each of the breast biopsytissues may be substantially equal to an inner width of a needle,through which a square or rectangular hole passes for receiving saideach of the breast biopsy tissues. The clinical or pathology parametersin the columns AI-AT of the subset data DB-2 are estrogen hormonereceptor positive (ER+), progesterone hormone receptor positive (PR+),HER2/neu hormone receptor positive (HER2/neu+), immunohistochemistrysubtype, path, BIRADS, Oncotype DX score, primary tumor (T), regionallymph nodes (N), distant metastasis (M), tumor size, and location. Formore information about the clinical or pathology parameters in thesubset data DB-2, please refer to FIGS. 17P through 17R. Other data orinformation in the big data database 70 may be added to the subset dataDB-2. For example, each of the data sets in the subset data DB-2 mayfurther include specific long chain mRNA biomarkers from next generationsequencing that are predictive of metastasis-free survival, such asHOTAIR, RP11-278 1.15.2-001, LINC00511-009, and AC004231.2-001. Each ofthe data sets in the subset data DB-2 may also include risk factors forcancer associated with the subject, such as smoking history, sunexposure, premalignant lesions, gene information or data, etc. Each ofthe data sets in the subset data DB-2 may also include imaging protocoldetails, such as MRI magnet strength, pulse sequence parameter, PETdosing, time at PET imaging, etc.

Referring to FIG. 1K, data in the column AC of the subset data DB-2 arevarious diameters, data in the column AD of the subset data DB-2 arevarious lengths, data in the column AE of the subset data DB-2 are thevarious numbers of MRI slices registered to respective regions,portions, locations or volumes of a breast biopsy tissue; data in thecolumn AF of the subset data DB-2 are various MRI area resolutions; datain the column AG of the subset data DB-2 are various MRI slicethicknesses. Alternatively, the diameters of all the breast biopsytissues in the column AC of the subset data DB-2 may be the same; thelengths of all the breast biopsy tissues in the column AD of the subsetdata DB-2 may be the same; all the data in the column AE of the subsetdata DB-2 may be the same; all the data in the column AF of the dataDB-2 may be the same; all the data in the column AG of the subset dataDB-2 may be the same.

A similar subset data like the subset data DB-1 or DB-2 may beestablished from the big data database 70 generating probability mapsfor brain cancer, liver cancer, lung cancer, rectal cancer, sarcomas,cervical cancer, or cancer metastasis to any organ such as liver, bone,and brain. In this case, the subset data may include multiple data sets,each of which may include: (1) measured values for MRI parameters (e.g.,those in the columns A-O, R, and S of the subset data DB-2) associatedwith a biopsy tissue (e.g., biopsied brain sample, biopsied liversample, biopsied lung sample, biopsied rectal sample, biopsied sarcomassample, or biopsied cervix sample) obtained from a subject (e.g.,human); (2) processed parameters (e.g., those in the columns P and Q ofthe subset data DB-2) associated with the biopsy issue; (3) a result orpathologist diagnosis of the biopsy tissue, such as cancer, normaltissue, or benign condition; (4) sample characters (e.g., those in thecolumns S-X of the subset data DB-1) associated with the biopsy tissue;(5) MRI characters (e.g., those in the columns Y, Z and AA of the subsetdata DB-1) associated with MRI slices registered to respective regions,portions, locations or volumes of the biopsy tissue; (6) a PET parameter(e.g., SUVmax depicted in FIG. 17I) associated with the biopsy tissue orthe subject; (7) CT parameters (e.g., HU and Hetwave) associated withthe biopsy tissue or the subject; (8) clinical or pathology parameters(e.g., those in the columns AB-AN of the subset data DB-1 or the columnsAI-AT of the subset data DB-2) associated with the biopsy tissue or thesubject; and (9) personal information (e.g., those in the columns AO-ARof the subset data DB-1) associated with the subject.

Description of Biopsy Tissue, MRI Slices Registered to the BiopsyTissue, and MRI Parameters for the Biopsy Tissue

Referring to FIG. 2A, a biopsy tissue or sample 90, such as any one ofthe biopsied tissues provided for the pathologist diagnosis depicted inthe big data database 70, any one of the prostate biopsy tissuesprovided for the pathologist diagnosis depicted in the subset data DB-1,or any one of the breast biopsy tissues provided for the pathologistdiagnosis depicted in the subset data DB-2, may be obtained from asubject (e.g., human) by core needle biopsy, such as MRI-guided needlebiopsy. Alternatively, an intra-operative incisional biopsy tissuesampling may be performed by a surgery to obtain the biopsy tissue 90from the subject. One or more fiducial markers that could be seen onsubsequent imaging may be placed during the surgery to match tissues oridentify positions of various portions of an organ with respect to theone or more fiducial markers. The fiducial marker is an object placed inthe field of view of an imaging system which appears in the imageproduced, for use as a point of reference.

The core needle biopsy is a procedure used to determine whether anabnormality or a suspicious area of an organ (e.g., prostate or breast)is a cancer, a normal tissue, or a benign condition or to determine anyother tissue characteristic such as mRNA expression, receptor status,and molecular tissue characteristics. With regard to MRI-guided needlebiopsy, magnetic resonance (MR) imaging may be used to guide a cylinderneedle to the abnormality or the suspicious area so that a piece oftissue, such as the biopsy tissue 90, is removed from the abnormality orthe suspicious area by the cylinder needle, and the removed tissue isthen sent to be examined by pathology.

During or before the core needle biopsy (e.g., MRI-guided needlebiopsy), parallel MRI slices SI₁ through SI_(N) registered to multiplerespective regions, portions, locations or volumes of the tissue 90 maybe obtained. The number of the registered MRI slices SI₁-SI_(N) mayrange from, equal to or greater than 2 up to, equal to or less than 10.The registered MRI slices SI₁-SI_(N) may have the same slice thicknessT, e.g., ranging from, equal to or greater than 1 millimeter up to,equal to or less than 10 millimeters, and more preferably ranging from,equal to or greater than 3 millimeters up to, equal to or less than 5millimeters.

Referring to FIGS. 2A and 2E, the biopsy tissue 90 obtained from thesubject by the cylinder needle may be long cylinder-shaped with a heighttT normalized to the slice thickness T and with a circular cross sectionperpendicular to its axial direction AD, and the circular cross sectionof the biopsy tissue 90 may have a diameter D1, perpendicular to itsheight tT extending along the axial direction AD, ranging from, equal toor greater than 0.5 millimeters up to, equal to or less than 4millimeters. The diameter D1 of the biopsy tissue 90 may besubstantially equal to an inner diameter of the cylinder needle, throughwhich a circular or round hole passes for receiving the biopsy tissue90. The axial direction AD of the tissue 90 to be biopsied may beparallel with the slice thickness direction of each of the MRI slicesSI₁-SI_(N). As shown in FIG. 2B, each of the MRI slices SI₁-SI_(N) mayhave an imaging plane 92 perpendicular to the axial direction AD of thetissue 90 to be biopsied, wherein an area of the imaging plane 92 is aside length W1 multiplied by another side length W2. The MRI slicesSI₁-SI_(N) may have the same area resolution, which is a field of view(FOV) of one of the MRI slices SI₁-SI_(N) (i.e., the area of its imagingplane 92) divided by the number of the machine-defined original pixelsin the imaging plane 92 of said one of the MRI slices SI₁-SI_(N).

Regions, i.e., portions, locations or volumes, of interest (ROIs) 94 ofthe respective MRI slices SI₁-SI_(N) are registered to and aligned withthe respective regions, portions, locations or volumes of the biopsytissue 90 to determine or calculate values of MRI parameters for theregions, portions, locations or volumes of the biopsy tissue 90. TheROIs 94 of the MRI slices SI₁-SI_(N) may have the same diameter,substantially equal to the diameter D1 of the biopsy tissue 90, i.e.,the inner diameter of the needle for taking the biopsy tissue 90, andmay have a total volume covering and substantially equaling the volumeof the biopsy tissue 90. As shown in FIG. 2C, the ROI 94 of each of theMRI slices SI₁-SI_(N) may cover or overlap multiple machine-definedoriginal pixels, e.g., 96 a through 96 f. A MRI parameter, i.e., C_(m)

_(n), (e.g., T1 mapping) for the ROI 94 of each of the MRI slicesSI₁-SI_(N) may be calculated or obtained by summing values of the MRIparameter for machine-defined original pixels p_(i)

_(j), i.e., 96 a-96 f, in said each of the MRI slices SI₁-SI_(N) weighedor multiplied by the respective percentages of areas A1, A2, A3, A4, A5and A6, overlapping with the respective machine-defined original pixels96 a-96 f in the ROI 94 of said each of the MRI slices SI₁-SI_(N),occupying the ROI 94 of said each of the MRI slices SI₁-SI_(N).Accordingly, a value for the MRI parameter for the whole biopsy tissue90 may be calculated or obtained by dividing the sum of the values forthe MRI parameter for the ROIs 94 of the MRI slices SI₁-SI_(N) by thenumber of the MRI slices SI₁-SI_(N). By this way, other MRI parameters(e.g., those in the columns B-O of the subset data DB-1 or those in thecolumns B-O, R and S of the subset data DB-2) for the whole biopsytissue 90 are obtained. The values for the various MRI parameters (e.g.,T1 mapping, T2 raw signal, T2 mapping, etc.) for the ROI 94 of each ofthe MRI slices SI₁-SI_(N) may be derived from different parameter mapsregistered to the corresponding region, portion, location or volume ofthe biopsy tissue 90. In an alternative example, the values for some ofthe MRI parameters for the ROI 94 of each of the MRI slices SI₁-SI_(N)may be derived from different parameter maps registered to thecorresponding region, portion, location or volume of the biopsy tissue90, and the values for the others may be derived from the same parametermap registered to the corresponding region, portion, location or volumeof the biopsy tissue 90. The aforementioned method for measuring the MRIparameters for the whole biopsy tissue 90 can be applied to each of theMRI parameters in the big data database 70 and the subset data DB-1 andDB-2.

Taking an example of T1 mapping, in the case of (1) four MRI slicesSI₁-SI₄ having four respective regions, portions, locations or volumesregistered to respective quarters of the biopsy tissue 90 and (2) theROI 94 of each of the MRI slices SI₁-SI₄ covering or overlapping the sixmachine-defined original pixels 96 a-96 f, values of T1 mapping for themachine-defined original pixels 96 a-96 f in each of the MRI slices SI₁-SI₄ and the percentages of the areas A1-A6 occupying the ROI 94 of eachof the MRI slices SI₁-SI₄ are assumed as shown in FIG. 2D. A value of T1mapping for the ROI 94 of the MRI slice SI₁, i.e., 1010.64, may beobtained or calculated by summing (1) the value, i.e., 1010, for themachine-defined original pixel 96 a multiplied by the percentage, i.e.,6%, of the area A1, overlapping with the machine-defined original pixel96 a in the ROI 94 of the MRI slice SI₁, occupying the ROI 94 of the MRIslice SI₁, (2) the value, i.e., 1000, for the machine-defined originalpixel 96 b multiplied by the percentage. i.e., 38%, of the area A2,overlapping with the machine-defined original pixel 96 b in the ROI 94of the MRI slice SI₁, occupying the ROI 94 of the MRI slice SI₁, (3) thevalue, i.e., 1005, for the machine-defined original pixel 96 cmultiplied by the percentage, i.e., 6%, of the area A3, overlapping withthe machine-defined original pixel 96 c in the ROI 94 of the MRI sliceSI₁, occupying the ROI 94 of the MRI slice SI₁, (4) the value, i.e.,1020, for the machine-defined original pixel 96 d multiplied by thepercentage, i.e., 6%, of the area A4, overlapping with themachine-defined original pixel 96 d in the ROI 94 of the MRI sliceSI_(i), occupying the ROI 94 of the MRI slice SI₁, (5) the value, i.e.,1019, for the machine-defined original pixel 96 e multiplied by thepercentage, i.e., 38%, of the area A5, overlapping with themachine-defined original pixel 96 e in the ROI 94 of the MRI slice SI₁,occupying the ROI 94 of the MRI slice SI₁, and (6) the value, i.e.,1022, for the machine-defined original pixel 96 f multiplied by thepercentage, i.e., 6%, attic area A6, overlapping with themachine-defined original pixel 96 f in the ROI 94 of the MRI slice SI₁,occupying the ROI 94 of the MRI slice SI₁. By this way, T1 mapping forthe ROIs 94 of the MRI slices SI₂, SI₃, and SI₄, i.e., 1006.94, 1022,and 1015.4, are obtained. Accordingly, T1 mapping for the whole biopsytissue 90, i.e., 1013.745, is obtained or calculated by dividing thesum, i.e., 4054.98 of T1 mapping for the ROIs 94 of the MRI slicesSI₁-SI₄ by the number of the MRI slices SI₁-SI₄, i.e., 4.

The volume of the long cylinder-shaped biopsied tissue 90 may betransformed into another shape which may have a volume the same or aboutthe same as the volume of the long cylinder-shaped biopsied tissue 90(or Volume of Interest (VOI), which may be π×Rn²×tT, where Rn is theradius of the biopsied tissue 90, and tT is the height of the biopsiedtissue 90), for easy or meaningful computing purposes, for medicalinstrumentation purposes or for clearer final data presentationpurposes. For example, referring to FIG. 2F, the long cylinder of thebiopsied tissue 90 with the radius Rn and height tT may be transformedinto a planar cylinder 98 to match the slice thickness T. The planarcylinder 98, having a volume, e.g., the same or about the same as theVOI of the biopsied tissue 90, may be defined by the following formula:π×Rn²×M×St=π×Rw²×pT, where Rn is the radius of the biopsy tissue 90(which is substantially equal to the inner radius of the needle fortaking the biopsy tissue 90). M is the number of the MRI slicesSI₁-SI_(N), St is the slice thickness T of the MRI slices SI₁- SI_(N).Rw is the radius of the planar cylinder 98, and pT is the height orthickness of the planar cylinder 98 perpendicular to the radius Rw ofthe planar cylinder 98. The height tT of the biopsy tissue 90 may besubstantially equal to the slice thickness T multiplied by the number ofthe MRI slices SI₁-SI_(N). In the invention, the height pT of the planarcylinder 98 is substantially equal to the slice thickness T, forexample. Accordingly, the planar cylinder 98 may have the height pTequal to the slice thickness T and the radius Rw equal to the radius Rnmultiplied by the square root of the number of the registered MRI slicesSI₁-SI_(N). The radius Rw of the planner cylinder 98 may be used todefine the radius Rm of a moving window MW in calculating probabilitymaps, e.g., illustrated in first through sixth embodiments, for apatient (e.g., human). Each of the biopsy tissue 90, the planar cylinder98 and the moving window MW may have a volume at least 2, 3, 5, 10 or 15times greater than that of each machine-defined original pixel of theMRI slices SI₁-SI_(N) and than that of each machine-defined originalpixel of an MRI image 10 from a subject (e.g., patient) depicted in astep S1 of FIG. 4. In addition, because the planar cylinder 98 istransformed from the biopsy tissue 90, the values of the MRI parametersfor the whole biopsy tissue 90 may be considered as those for the planarcylinder 98.

Further, each of biopsy tissues provided for pathologist diagnoses in asubset data, e.g., DB-1 or DB-2, of the big data database 70 may have acorresponding planar cylinder 98 with its radius Rw, and data (such aspathologist diagnosis and values of imaging parameters) for said each ofthe biopsy tissues in the subset data, e.g., DB-1 or DB-2, of the bigdata database 70 may be considered as those for the corresponding planarcylinder 98. Statistically, the moving window MW may be determined withthe radius Rm, perpendicular to a thickness of the moving window MW,bawd on the statistical distribution or average of the radii Rw of theplanar cylinders 98 transformed from the volumes of the biopsy tissuesprovided for the pathologist diagnoses in the subset data, e.g., DB-1 orDB-2, of the big data database 70. In the invention, each of the biopsytissues provided for the pathologist diagnoses in the subset data, e.g.,DB-1 or DB-2, of the big data database 70, for example, may have avolume, i.e., VOI, substantially equal to the volume of the movingwindow MW to be used in calculating one in more probability maps. Inother words, the volume of the biopsy tissue, i.e., VOI, defines thesize (e.g., the radius Rm) of the moving window MW to be used incalculating one or more probability maps.

Each of the prostate biopsy tissues provided for the pathologistdiagnoses in the subset data DB-1 may be referred to the illustration ofthe biopsy tissue 90. In the column W of the subset data DB-1, thediameter of each of the prostate biopsy tissues may be referred to theillustration of the diameter D1 of the biopsy tissue 90. The MRI slicesregistered to the respective regions, portions, locations or volumes ofeach of the prostate biopsy tissues provided for the pathologistdiagnoses in the subset data DB-1 may be referred to the illustration ofthe MRI slices SI₁-SI_(N) registered to the respective regions,portions, locations or volumes of the biopsy tissue 90. The values ofthe MRI parameters for each of the prostate biopsy tissues, i.e., foreach of the corresponding planar cylinders 98, in the respective columnsA-O of the subset data DB-1 may be calculated as the values of the MRIparameters for the whole biopsy tissue 90, i.e., for the planar cylinder98 transformed from the volume of the biopsy tissue 90, are calculated.In the column Z of the subset data DB-1, the MRI slices registered tothe respective regions, portions, locations or volumes of each of theprostate biopsy tissues may have the same area resolution, which may bereferred to the illustration of the area resolution of the MRI slicesSI₁-SI_(N) registered to the respective regions, portions, locations orvolumes of the biopsy tissue 90. In the column AA of the subset dataDB-1, the MRI slices registered to the respective regions, portions,locations or volumes of each of the prostate biopsy tissues may have thesame slice thickness, which may be referred to the illustration of theslice thickness T of the MRI slices SI₁-SI_(N).

In the column S of the subset data DB-1, the percentage of cancer forthe whole volume of the prostate biopsy tissue in each of all or some ofthe data sets may be replaced by the percentage of cancer for a partialvolume of the prostate biopsy tissue, a MRI slice is imaged for andregistered to the partial volume of the prostate biopsy tissue. In thiscase, the MRI parameters, in the columns A-O of the subset data DB-1,that are in said each of all or some of the data sets are shown for aROI of the MRI slice registered to the partial volume of the prostatebiopsy tissue. The ROI of the MRI slice covers or overlaps multiplemachine-defined original pixels in the MRI slice, and each of the MRIparameters for the ROI of the MRI slice may be calculated by summingmeasured values of said each of the MRI parameters for themachine-defined original pixels weighed or multiplied by respectivepercentages of areas, overlapping with the respective machine-definedoriginal pixels in the ROI of the MRI slice, occupying the ROI of theMRI slice. Multiple values for the MRI parameters for the ROI of the MRIslice may be derived from different parameter maps registered to thepartial volume of the prostate biopsy tissue. In an alternative example,the values for some of the MRI parameters for the ROI of the MRI slicemay be derived from different parameter maps registered to the partialvolume of the prostate biopsy tissue, and the values for the others maybe derived from the same parameter map registered to the partial volumeof the prostate biopsy tissue.

Each of the breast biopsy tissues provided for the pathologist diagnosesin the subset data DB-2 may be referred to the illustration of thebiopsy tissue 90. In the column AC of the subset data DB-2, the diameterof each of the breast biopsy tissues may be referred to the illustrationof the diameter D1 of the biopsy tissue 90. The MRI slices registered tothe respective regions, portions, locations or volumes of each of thebreast biopsy tissues provided for the pathologist diagnoses in thesubset data DB-2 may be referred to the illustration of the MRI slicesSI₁-SI_(N) registered to the respective regions, portions, locations orvolumes of the biopsy tissue 90. The values of the MRI parameters foreach of the breast biopsy tissues, i.e., for each of the correspondingplanar cylinders 98, in the respective columns A-O, R, and S of thesubset data DB-2 may be calculated as the values of the MRI parametersfor the whole biopsy tissue 90, i.e., for the planar cylinder 98transformed from the volume of the biopsy tissue 90, are calculated. Inthe column AF of the subset data DB-2, the MRI slices registered to therespective regions, portions, locations or volumes of each of the breastbiopsy tissues may have the same area resolution, which may be referredto the illustration of the area resolution of the MRI slices SI₁-SI_(N)registered to the respective regions, portions, locations or volumes ofthe biopsy tissue 90. In the column AG of the subset data DB-2, the MRIslices registered to the respective regions, portions, locations orvolumes of each of the breast biopsy tissues may have the same slicethickness, which may be referred to the illustration of the slicethickness T of the MRI slices SI₁-SI_(N).

In the column AB of the subset data DB-2, the percentage of cancer forthe whole volume of the breast biopsy tissue in each of all or some ofthe data sets may be replaced by the percentage of cancer for a partialvolume of the breast biopsy tissue, a MRI slice is imaged for andregistered to the partial volume of the breast biopsy tissue. In thiscase, the MRI parameters, in the columns A-O, R, and S of the subsetdata DB-2, that are in said each of all or some of the data sets areshown for a ROI of the MRI slice registered to the partial volume of thebreast biopsy tissue. The ROI of the MRI slice covers or overlapsmultiple machine-defined original pixels in the MRI slice, and each ofthe MRI parameters for the ROI of the MRI slice may be calculated bysumming measured values of said each of the MRI parameters for themachine-defined original pixels weighed or multiplied by respectivepercentages of areas, overlapping with the respective machine-definedoriginal pixels in the ROI of the MRI slice, occupying the ROI of theMRI slice. Multiple values for the MRI parameters for the ROI of the MRIslice may be derived from different parameter maps registered to thepartial volume of the breast biopsy tissue. In an alternative example,the values for some of the MRI parameters for the ROI of the MRI slicemay be derived from different parameter maps registered to the partialvolume of the breast biopsy tissue, and the values for the others may bederived from the same parameter map registered to the partial volume ofthe breast biopsy tissue.

In an alternative example, the biopsied tissue 90 may be obtained by aneedle with a square through hole therein. In this case, the biopsiedtissue 90 may hove a longitudinal shape with a square-shapedcross-section having a width Wb (which is substantially equal to aninner width of the needle, i.e., the width of the square through hole ofthe needle) and a height Ht (which is substantially equal to, e.g., theslice thickness T multiplied by the number of the MRI slicesSI₁-SI_(N)). The volume of the biopsied tissue 90 may be transformedinto a flat square FS with a width Wf and a thickness or height fT. Theflat square FS, having a volume the same or about the same as the volumeof the biopsied tissue 90 (or Volume of Interest (VOI), which may be theheight Ht multiplied by the square of the width Wb), may be defined bythe following formula: Wb²×M×St=Wf²×fT, where Wb is the width of thebiopsy tissue 90, M is the number of the MRI slices SI₁-SI_(N), St isthe slice thickness T of the MRI slices SI₁-SI_(N), Wf is the width ofthe flat square FS, and fT is the height or thickness of the flat squareFS perpendicular to the width Wf of the flat square FS. In theinvention, the height or thickness fT of the flat square FS issubstantially equal to the slice thickness T, for example. Accordingly,the flat square FS may have the height or thickness fT equal to theslice thickness T and the width Wf equal to the width Wb multiplied bythe square root of the number of the registered MRI slices SI₁-SI_(N).In the case of the moving window MW with a square shape, the width Wf ofthe flat square FS may be used to define the width of the moving windowMW in calculating probability maps. Each of the biopsy tissue 90, theflat square FS and the square moving window MW may have a volume atleast 2, 3, 5, 10 or 15 times greater than that each machine-definedoriginal pixel of the MRI slices SI₁-SI_(N) and than that of eachmachine-defined original pixel of an MRI image, e.g., 10 from a subject(e.g., patient) depicted in a step S1 of FIG. 4. Further, each of biopsytissues provided for pathologist diagnoses in a subset data of the bigdata database 70 may have a corresponding flat square FS with its widthWf, and data (such as pathologist diagnosis and measured values ofimaging parameters) for said each of the biopsy tissues in the subsetdata of the big data database 70 may be considered as those for thecorresponding flat square FS.

Description of Area Resolution and Machine-Defined Original Pixels of aSingle MRI Slice

In the invention, an area resolution of a single MRI slice such assingle slice MRI image 10 shown in FIG. 5 or 16 is a field of view (FOV)of the single MRI slice divided by the number of all machine-definedoriginal pixels in the FOV of the single MRI slice. Each of the voxelsof the single MRI slice may have a pixel (or pixel plane), perpendicularto the slice thickness direction of the single MRI slice, having asquare area with the same four side lengths.

Description of Moving Window and Probability Map

Any probability map in the invention may be composed of multiplecomputation pixels with the same size, which are basic units of theprobability map. The see of the computation pixels used to compose theprobability map may be defined based on the size of the moving windowMW, which is determined or defined based on information data associatedwith the biopsy tissues provided for the pathologist diagnoses in thesubset data. e.g., DB-1 or DB-2, of the big data database 70. Theinformation data, for example, may include the radii Rw of planarcylinders 98 transformed from the volumes of the biopsy tissues. Inaddition, each of the computation pixels of the probability map may havea volume or size equal to, greater than or less than that of anymachine-defined original pixel in a single MRI slice, such as MRI image10 shown in FIG. 5 or 16, depicted in steps S1-S6 of FIG. 4.

The moving window MW may have various shapes, such as a circular shape,a square shape, a rectangular shape, a hexagonal shape, or an octagonalshape. In the invention, referring to FIG 3A, the moving window MW is acircular moving window 2 with a radius Rm, for example. The radius Rm ofthe circular moving window 2 may be calculated, determined, or definedbased on the statistical distribution or average of the radii Rw ofplanar cylinders 98 obtained from biopsy tissues associated with asubset data, e.g., DB-1 or DB-2, of the big data database 70. Forexample, in the first embodiment of the invention, the radius Rm of thecircular moving window 2 may be calculated, determined or defined basedon the statistical distribution or average of the radii Rw of the planarcylinders 98 obtained from the prostate biopsy tissues associated withthe subset data DB-1; the approach to obtain the radius Rw of the planarcylinder 98 from the biopsy tissue 90 may be applied to obtain the radiiRw of the planar cylinders 98 from the prostate biopsy tissuesassociated with the subset data DB-1. In the third embodiment of theinvention, the radius Rm of the circular moving window 2 may becalculated, determined or defined based on the statistical distributionor average of the radii Rw of the planar cylinders 98 obtained from thebreast biopsy tissues associated with the subset data DB-2; the approachto obtain the radius Rw of the planar cylinder 98 from the biopsy tissue90 may be applied to obtain the radii Rw of the planar cylinders 98 fromthe breast biopsy tissues associated with the subset data DB-2.

Referring to FIG. 3A, 3B or 3C, a square 4 having its four verticeslying on the circular moving window 2, i.e., the biggest square 4inscribed in the circular moving window 2, is defined and divided intomultiple small units or grids 6. The small grids 6 may be n² smallsquares each having a width Wsq, where n is an integer, such as 2, 3, 4,5, 6, or more than 6. Based on the size (e.g., the width Wsq) and shapeof the divided squares 6, the size and shape of the computation pixelsused to compose the probability map may be defined. In other words, eachof the computation pixels used to compose the probability map, forexample, may be defined as a square with the width Wsq and a volume thesame or about the same as that of each square 6 based on the radius Rmof the circular moving window 2 and the number of the squares 6 in thecircular moving window 2, i.e., based on the width Wsq of the squares 6in the circular moving window 2.

The circular moving window 2 in FIG. 3A is shown with a two-by-twosquare array in the square 4, each square 6 of which has the same area(i.e., a quarter of the 4) In FIG. 3A, the four non-overlapped squares 6have the same width Wsq, which is equal to the radius km of the circularmoving window 2 divided by √{square root over (2)}. In the case of thecircular moving window 2 having the radius Rm of √{square root over (2)}millimeters, each square 6 may have an area of 1 millimeter by 1millimeter, that is, each square 6 has the width Wsq of 1 millimeter.

In an alternative example, referring to FIG. 3B, the square 4 may have athree-by-three square array, each square 6 of which has the same area(i.e., a ninth of the square 4), the nine non-overlapped squares 6 havethe same width Wsq, which is equal to the radius Rm of the circularmoving window 2 divided by ⅔√{square root over (2)}. In an alternativeexample, referring to FIG. 3C, the square 4 may have a four-by-foursquare array, each square 6 of which has the same area (i.e., onesixteenth of the square 4); the sixteen non-overlapped squares 6 havethe same width Wsq, which is equal to the radius Rm of the circularmoving window 2 divided by 2√{square root over (2)}.

Accordingly, the moving window MW (e.g., the circular moving window 2)may be defined to include four or more non-overlapped grids 6 having thesame square shape, the same size or area (e.g., 1 millimeter by 1millimeter), and the same width Wsq, e.g., equal to, greater than orless than any side length of machine-defined original pixels in a singleMRI slice, such as MRI image 10 shown in FIG. 5 or 16, depicted in thesteps S1-S3 of FIG. 4. Each of the squares 6, for example. may have anarea less than 25% of that of the moving window MW and equal to, greaterthan or less than that of each machine-defined original pixel of thesingle MRI slice; each of the squares for example, may have a volumeequal to, greater than or less than that of each machine-definedoriginal pixel of the single MRI slice. In the case of the moving windowMW defined to include four or more nun-overlapped squares 6 with thewidth Wsq, the moving window MW may move across the single MRI slice ata regular step or interval of a fixed distance of the width Wsq in the xand y directions so that the computation pixels of the probability mapare defined. A stop of the moving window MW overlaps the neighboringslop of the nerving window MW.

Alternatively, the grids 6 may be n rectangles each having a width Wrecand a length Lrec, where n is an integer, such as 2, 3, 4, 5, 6, 7, 8,or more than 8. Based on the size (e.g., the width Wrec and the lengthLrec) and shape of the divided rectangles 6, the size and shape of thecomputation pixels used to compose the probability map may be defined.In other words, each of the computation pixels used to compose theprobability map, for example, may be defined as a rectangle with thewidth Wrec, the length Lrec, and a volume the same or about the same asthat of each rectangle 6 based on the radius Rm of the circular movingwindow 2 and the number of the rectangles 6 in the circular movingwindow 2, i.e., based on the width Wrec and length Lrec of therectangles 6 in the circular moving window 2. Accordingly, the movingwindow MW (e.g., the circular moving window 2) may be defined to includefour or more non-overlapped grids 6 having the same rectangle shape, thesame size or area, the same width Wrec, e.g., equal to, greater than orless than any side length of machine-defined original pixels to a singleMRI slice, such as MRI image 10 shown in FIG. 5 or 16, depicted in thesteps S1-S3 of FIG. 4, and the same length Lrec, e.g., equal to, greaterthan or less than any side length of the machine-defined original pixelsin the single MRI slice. Each of the rectangles 6, for example, may havean area less than 25% of that of the moving window MW and equal to,greater than or less than that of each machine-defined original pixel ofthe single MRI slice. Each of the rectangles 6, for example, may have avolume equal to, greater than or less than that of each machine-definedoriginal pixel of the single MRI slice. In the case of the moving windowMW defined to include four or more non-overlapped rectangles 6 with thewidth Wrec and the length Lrec, the moving window MW may move across thesingle MRI slice at a regular step or interval of a fixed distance ofthe width Wrec in the x direction and at a regular step or interval of afixed distance of the length Lrec in the y direction so that thecomputation pixels of the probability map are defined. A stop of themoving window MW overlaps the neighboring stop of the moving window MW.

In the case of the moving window MW with a square shape, the squaremoving window MW may be determined with a width Wsm based on thestatistical distribution or average of the widths Wf of flat squares FSobtained from biopsy tissues associated with a subset data of the bigdata database 70. The square moving window MW may be divided into theaforementioned small grids 6. In this case, each of the computationpixels of the probability map, for example, may be defined as a squarewith the width Wsq and a volume the same or about the same as that ofeach square 6 based on the width Wsm of the square moving window MW andthe number of the squares 6 in the square moving window MW, i.e., basedon the width Wsq of the squares 6 in the square moving window MW.Alternatively, each of the computation pixels of the probability map maybe defined as a rectangle with the width Wrec, the length Lrec, and avolume the same or about the same as that of each rectangle 6 based onthe width Wsm of the square moving window MW and the number of therectangles 6 in the square moving window MW, based on the width Wrec andlength Lrec of the rectangles 6 in the square moving window MW.

Description of Classifier CF

The classifier CF for an event, such as biopsy-diagnosed tissue or tumorcharacteristic for, e.g., specific cancerous cells or occurrence ofprostate cancer or breast cancer, may be created or established based ona subset (e.g., the subset data DB-1 or DB-2 or the aforementionedsubset data established for generating the voxelwise or pixelwiseprobability map of brain cancer, liver caner, lung cancer, rectalcancer, sarcomas, cervical cancer, or cancer metastasis to any organsuch as liver, bone, and brain) obtained from the big data database 70.The subset may have all data associated with the given event from thebig data database 70. The classifier CF may be a Bayesian classifier,which may be created by performing the following steps: constructingdatabase, preprocessing parameters, ranking parameters, identifying atraining dataset, and determining posterior probabilities for test data.

In the step of constructing database, a first group and a second groupmay be determined or selected from a tissue-based or biopsy-based subsetdata, such as the aforementioned subset data, e.g., DB-1 or DB-2, fromthe big data database 70, and various variables associated with each ofthe first and second groups are obtained from the tissue-based orbiopsy-based subset data. The variables may be MRI parameters in thecolumns A-O of the subset data DB-1 or the columns A-O, R, and S of thesubset data DB-2. Alternatively, the variables may be T1 mapping, T2 rawsignal, T2 mapping, delta Ktrans, tau, Dt IVIM, fp IVIM, ADC (highb-values). R*, Ktrans from TM, Ktrans from ETM, Ktrans from SSM, Ve fromTM, Ve from ETM, Ve from SSM, and standard PET.

The first group, for example, may be associated with a first data typeor feature in a specific column of the subset data DB-1 or DB-2, and thesecond group may be associated with a second data type or feature in thespecific column of the subset data DB-1 or DB-2, wherein the specificcolumn of the subset data DB-1 or DB-2 may be one of the columns R-AR ofthe subset data DB-1 or one of the columns AA-AX of the subset dataDB-2. In a first example, the first data type is associated withprostate cancer in the column R of the subset data DB-1, and the seconddata type is associated with non-prostate cancer (e.g., normal tissueand benign condition) in the column R of the subset data DB-1. In asecond example, the first data type is associated with breast cancer inthe column AA of the subset data DB-2, and the second data type isassociated with non-breast cancer (e.g., normal tissue and benigncondition) in the column AA of the subset data DB-2. In the case of thefirst group associated with a cancer type (e.g., prostate cancer orbreast cancer) and the second group associated with a non-cancer type(e.g., non-prostate cancer or non-breast cancer), the cancer type mayinclude data or interest for a single parameter, such as malignancy,mRNA expression, etc., and the non-cancer type may include normal tissueand benign conditions. The benign conditions may vary based on tissues.For example, the benign conditions for breast tissues may includefibroadenomas, cysts, etc.

In a third example, the first data type is associated with one ofGleason scores 0 through 10, such as Gleason score 5, in the column T ofthe subset data DB-1, and the second data type is associated with theothers of Gleason scores 0 through 10, such as Gleason scores 0 through4 and 6 through 10, in the column T of the subset data DB-1. In a fourthexample, the first data type is associated with two or more of Gleasonscores 0 through 10, such as Gleason scores greater than 7, in thecolumn T of the subset data DB-1, and the second data type is associatedwith the others of Gleason scores 0 through 10, such as Gleason scoresequal to and less than 7, in the column T of the subset data DB-1. In afifth example, the first data type is associated with the percentage ofcancer in a specific range from a first percent (e.g., 91 percent) to asecond percent (e.g., 100 percent) in the column S of the subset dataDB-1, and the second data type is associated with the percentage ofcancer beyond the specific range in the column S of the subset dataDB-1. In a sixth example, the first data type is associated with a smallcell subtype in the column AE of the subset data DB-1, and the seconddata type is associated with a non-small cell subtype in the column AEof the subset data DB-1. Any event depicted in the invention may be theabove-mentioned first data type or feature, occurrence of prostatecancer, occurrence of breast cancer, or a biopsy-diagnosed tissue ortumor characteristic for, e.g., specific cancerous cells.

After the step of constructing database is completed, the step ofpreprocessing parameters is performed to determine what the variablesare conditionally independent. A technique for dimensionality reductionmay allow reduction of some of the variables that are conditionallydependent to a single variable. Use of dimensionality reductionpreprocessing of data may allow optimal use of all valuable informationin datasets. The simplest method for dimensionality reduction may besimple aggregation and averaging of datasets. In one example,aggregation may be used for dynamic contrast-enhanced MRI (DCE-MRI)datasets. Ktrans and Ve measured values from various differentpharmacokinetic modeling techniques may be averaged to reduce errors andoptimize sensitivity to tissue change.

For the variables, averaging and subtraction may be used to consolidatemeasured variables. Accordingly, five or more types of parameters may beselected or obtained from the variables. The five or more selectedparameters are conditionally independent and may include T1 mapping, T2mapping, delta Ktrans (obtained by subtracting “Ktrans from Tofts Model”from “Ktrans from Shutterspeed Model”), tau, Dt IVIM, fp IVIM, R*,average Ve, and average Ktrans in the respective columns A, C-G, J, P,and Q of the subset data DB-1 or DB-2. Alternatively, the five or moreselected parameters may include T1 mapping, T2 mapping, delta Ktrans,tau, fp IVIM, R*, average Ve, average Ktrans, standard PET and aparameter D obtained by averaging Dt IVIM and ADC thigh b-values),wherein the parameter D is conditionally independent of every otherselected parameter.

After the step of preprocessing parameters is complete, the step ofranking parameters is performed to determine the optimal ones of thefive or more selected parameters for use in classification, e.g., tofind the optimal parameters that are most likely to give the highestposterior probabilities, so that a rank list of the five or moreselected parameters is obtained. A filtering method, such as t-test, maybe to look for an optimal distance between the first group (indicated byGR1) and the second group (indicated by GR2) for every one of the fiveor more selected parameters, as shown in FIG. 21. FIG. 21 shows twoGaussian curves of two given different groups (i.e., the first andsecond groups GR1 and GR2) with respect to parameters. In FIG. 21, Xaxis is values for a specific parameter, and Y axis is the number oftissue biopsies.

Four different criteria may be computed for ranking the five or moreselected parameters. The first criterion is the p-value derived from at-test of the hypothesis that the two features sets, corresponding tothe first group and the second group, coming from distributions withequal means. The second criterion is the mutual information (MI)computed between the classes and each of the first and second groups.The last two criteria are derived from the minimum redundancy maximumrelevance (mRMR) selection method.

In the step of identifying a training dataset, a training dataset of thefirst group and the second group is identified based on the rank listafter the step of ranking parameters, and thereby the Bayesianclassifier may be created based on the training dataset of the firstgroup and the second group. In the step of determining posteriorprobabilities for test data, the posterior probabilities for the testdata may be determined using the Bayesian classifier. Once the Bayesianclassifier is created, the test data may be applied to predict posteriorprobabilities for high resolution probability maps.

In an alternative example, the classifier CF may be a neural network(e.g., probabilistic neural network, single-layer feed forward neuralnetwork, multi-layer perception neural network, or radial basis functionneural network), a discriminant analysis, a decision tree (e.g.,classification and regression tree, quick unbiased and efficientstatistical tree, Chi-square automatic interaction detector, C5.0, orrandom finest decision tree), an adaptive boosting, a k-nearestneighbors algorithm, or a support vector machine. In this case, theclassifier CF may be created based on information associated with thevarious MRI parameters for the ROIs 94 of the MRI slices S1 ₁-SI_(N)registered to each of the biopsy tissues depicted in the subset dataDB-1 or DB-2.

First Embodiment

After the big data database 70 and the classifier CF are created orconstructed, a (voxelwise or pixelwise) probability map (i.e., adecision data map), composed of multiple computation pixels with thesame size, for an event (i.e., a decision-making characteristic) may begenerated or constructed for, e.g., evaluating or determining the healthstatus of a subject such as healthy individual or patient, the physicalcondition of an organ or other structure inside the subject's body, orthe subject's progress and therapeutic effectiveness by sequentiallyperforming six steps S1 through S6 illustrated in FIG. 4. The stepsS1-S6 may be performed based on the moving window MW with a suitableshape such as a circular shape, a square shape, a rectangular shape, ahexagonal shape, or an octagonal shape. The moving window MW is selectedfor a circular shape, i.e., the circular moving window 2, to perform thesteps S1-S6 as mentioned in the following paragraphs. Referring to FIG.4, in the step S1, a MRI image ID (single slice) shown in FIG. 5 isobtained from the subject by a MRI device or system. The MRI image 10(i.e., a molecular image) is composed of multiple machine-definedoriginal pixels in its field of view (FOV) to show an anatomical regionof the subject, such as prostate. In an alternative embodiment, the MRIimage 10 may show another anatomical region of the subject, such asbreast, brain, liver, lung, cervix, bone, sarcomas, metastatic lesion orsize, capsule around the prostate, pelvic lymph nodes around theprostate, or lymph node.

In the step S2, a desired or anticipated region 11, i.e., target region,is determined on the MRI image 10, and a computation region 12 for theprobability map is set in the desired or anticipated region 11, i.e.,target region, of the MRI image 10 and defined with the computationpixels based on the size (e.g., the radius Rm) of the moving window 2and the size and shape of the small grids 6 in the musing window 2 suchas the width Wsq of the small squares 6 or the width Wrec and the lengthLrec of the small rectangles 6. A side length of the computation region12 in the x direction, for example, may be calculated by obtaining afirst maximum positive integer of a side length of the desired oranticipated region 11, i.e., target region, in the x direction dividedby the width Wsq of the small squares 6 in the moving window 2, andmultiplying the width Wsq by the first maximum positive integer, a sidelength of the computation region 12 in the y direction may be calculatedby obtaining a second maximum positive integer of a side length of thedesired or anticipated region 11, i.e., target region, in the ydirection divided by the width Wsq of the small squares 6 in the movingwindow 2, and multiplying the width Wsq by the second maximum positiveinteger. Alternatively, a side length of the computation region 12 inthe x direction may be calculated by obtaining a first maximum positiveinteger of a side length of the desired or anticipated region 11, i.e.,target region, in the x direction divided by the width Wrec of the smallrectangles 6 in the moving window 2, and multiplying the width Wrec bythe first maximum positive integer, a side length of the computationregion 12 in the y direction may be calculated by obtaining a secondmaximum positive integer of a side length of the desired or anticipatedregion 11, i.e., target region, in the y direction divided by the lengthLrec of the small rectangles 6 in the moving window 2, and multiplyingthe length Lrec by the second maximum positive integer. The computationregion 12 may cover at least 10, 25, 50, 80, 90 or 95 percent of the FOVof the MRI image 10, which may include the anatomical region of thesubject. The computation region 12, for example, may be shaped like aparallelogram such as square or rectangle.

The size and shape of the computation pixels used to compose theprobability map, for example, may be defined based on the radius Rm ofthe moving window 2, wherein the radius Rm is calculated based on, e.g.,the statistical distribution or average of the radii Rw of the planarcylinders 98 transformed from the volumes of the prostate biopsy tissuesprovided for the pathologist diagnoses depicted in the subset data DB-1,as illustrated in the section of “description of moving window andprobability map”. Each of the computation pixels, for example, may bedefined as a square with the width Wsq in the case of the moving window2 defined to include the small squares 6 each having the width Wsq.Alternatively, each of the computation pixels may be defined as arectangle with the width Wrec and the length Lrec in the case of themoving window 2 defined to include the small rectangles 6 each havingthe width Wrec and the length Lrec.

A step for abbreviated search functions (such as looking for one or morespecific areas of the MRI image 10 where diffusion signals are above acertain signal value) may be performed between the steps S1 and S2, andthe computation region 12 may cover the one or more specific areas ofthe MRI image 10. For clear illustration of the following steps, FIGS.6A and 6B show the computation region 12 without the MRI image 10.Referring to FIG. 6A, in the step S3 of FIG. 4, after the computationregion 12 and the size and shape of the computation pixels of theprobability map are defined or determined, the stepping of the movingwindow 2 and the overlapping between two neighboring stops of the movingwindow 2 are determined. In the step S3, the moving window 2,illustrated in FIG. 3A, 3B or 3C for example, moves across thecomputation region 12 at a regular step or interval of a fixed distancein the x and y directions, and values of specific MRI parameters (each,for example, may be the mean or a weighted mean) for each stop of themoving window 2 for the computation region 12 may be derived or obtainedfrom the MRI image 10 or a registered imaging dataset including, e.g.,the MRI image 10 and different MRI parameter maps registered to the MRIimage 10. In an alternative example, the values for some of the specificMRI parameters for each stop of the moving window 2 may be derived fromdifferent MRI parameter maps registered to the MRI image 10, and thevalues for the others may be derived from the same parameter mapregistered to the MRI image 10. The fixed distance in the x directionmay be substantially equal to the width Wsq in the case of thecomputation pixels defined as the squares with the width Wsq or may besubstantially equal to the width Wrec in the case of the computationpixels defined as the rectangles with the width Wrec and the lengthLrec. The fixed distance in the y direction may be substantially equalto the width Wsq in the case of the computation pixels defined as thesquares with the width Wsq or may be substantially equal to the lengthLrec in the case of the computation pixels defined as the rectangleswith the width Wrec and the length Lrec.

For more elaboration, referring to FIGS. 6A and 6B, the moving window 2may start at a corner Cx of the computation region 12. In the beginningof moving the moving window 2 across the computation region 12, thesquare 4 inscribed in the moving window 2 may have a corner Gx alignedwith the corner Cx of the computation region 12. In other words, thesquare 4 inscribed in the moving window 2 has an upper side 401 alignedwith an upper side 121 of the computation region 12 and a left side 402aligned with a left side 122 of the computation region 12. Iwoneighboring stops of the moving window 2 that are shifted from eachother by the fixed distance in the x or y direction may partiallyoverlap with each other, and the ratio of the overlap of the twoneighboring stops of the moving window 2 to the area of any one of thetwo neighboring stops of the moving window 2 may range from, equal to orgreater than 50 percent up to, equal to or less than 99 percent.

The specific MRI parameters for each stop of the moving window 2 mayinclude T1 mapping, T2 raw signal, T2 mapping, delta Ktrans, tau, DtIVIM, fp IVIM, ADC (high b-values), nADC (high b-values). R*, Ktransfrom TM, ETM and SSM, and Ve from TM and SSM, which may be referred tothe types of the MRI parameters in the columns A-O of the subset dataDB-1, respectively. Alternatively, the specific MRI parameters for eachstop of the moving window 2 may include four or more of the following:T1 mapping, T2 raw signal, T2 mapping, Ktrans from TM, ETM, and SSM, Vefrom TM and SSM, delta Ktrans, tau, ADC (high b-values), nADC (highb-values). Dt IVIM, fp IVIM, and R*. The specific MRI parameters ofdifferent modalities may be obtained from registered (multi-parametric)image sets (or the MRI parameter maps in the registered(multi-parametric) image dataset), and rigid and non-rigid standardregistration techniques may be used to get each section of anatomy intothe same exact coordinate location on each of the registered(multi-parametric) image sets (or on each of the MRI parameters maps).

Referring to FIG. 7A, the moving window 2 at each stop may cover oroverlap multiple machine-defined original pixels p_(i)

_(j) e.g., 14 a-14 f, in the computation region 12, of the MRI image 10.A MRI parameter C_(m)

_(n) such as T1 mapping for each stop of the moving window 2 may becalculated by summing values of the MRI parameters for themachine-defined original pixels p_(i)

_(j), e.g., 14 a-14 f, weighed to multiplied by the respectivepercentages of areas B1, B2, B3, B4, B5 and B6, overlapping with therespective machine-defined original pixels p_(i)

_(j), i.e., 14 a-14 f, in the moving window 2, occupying the movingwindow 2. By this way, other MRI parameters C_(m)

_(n) (e.g., those in the columns B-O of the subset data DB-1) for eachstop W_(m)

_(n) of the moving window 2 are calculated. Taking an example of T1mapping, in the case of the moving window 2 at a certain stop, values ofT1 mapping for the machine-defined original pixels p_(i)

_(j), i.e., 14 a-14 f, and the percentages of the areas B1-B6 occupyingthe moving window 2 are assumed as shown in FIG. 7B. A value C_(m)

_(n) i.e., 1010.64, of T1 mapping for the stop W_(m)

_(n) of the moving window 2 may be obtained or calculated by summing (1)the value, i.e., 1010, of T1 mapping for the machine-defined originalpixel 14 a multiplied by the percentage, i.e., 6%, of the area B1,overlapping with the machine-defined original pixel 14 a in the movingwindow 2, occupying the moving window 2, (2) the value i.e., 1000, of T1mapping for the machine-defined original pixel 14 b multiplied by thepercentage, i.e., 38%, of the area B2, overlapping with themachine-defined original pixel 14 b in the moving window 2, occupyingthe moving window 2, (3) the value, i.e., 1005, of T1 mapping for themachine-defined original pixel 14 c multiplied by the percentage, i.e.,6%, of the area B3, overlapping with the machine-defined original pixel14 c in the moving window 2, occupying the moving window 2, (4) thevalue, i.e., 1020, of T1 mapping for the machine-defined original pixel14 d multiplied by the percentage, i.e., 6% of the area B4, overlappingwith the machine-defined original pixel 14 d in the moving window 2,occupying the moving window 2, (5) the value, i.e., 1019, of T1 mappingfor the machine-defined original pixel 14 e multiplied by thepercentage, i.e., 38%, of the area B5, overlapping with themachine-defined original pixel 14 e in the moving window 2, occupyingthe moving window 2, and (6) the value, i.e., 1022, of T1 mapping forthe machine-defined original pixel 14 f multiplied by the percentage,i.e., 6%, of the area B6, overlapping with the machine-defined originalpixel 14 f in the moving window 2, occupying the moving window 2. In theabove description, the measure of each of the specific MRI parametersfor each stop of the moving window 2 is the arithmetic weighted averageof measures, for said each of the specific MRI parameters, for thepixels, e.g., 14 a-14 f of the MRI image 10 overlapping with said eachstop of the moving window 2. That is, the measure of each of the speakMRI parameters, for the pixels, e.g., 14 a-14 f of the MRI image 10 isuniform inside each pixel. Alternatively, the value C_(m)

_(n) of each of the specific MRI parameters for each stop W_(m)

_(n) of the moving window 2 may be the Gaussian weighted average ofmeasured values, for said each of the specific MRI parameters, for themachine-defined original pixels p_(i)

_(j), e.g., 14 a-14 f, of the MRI image 10 overlapping with said eachstop W_(m)

_(n) of the moving window 2. That is, the measure of each of thespecific MRI parameters, for the pixels, e.g., 14 a-14 f of the MRIimage 10 is Gaussian distributed inside each pixel.

The registered imaging dataset may be created for the subject toinclude, e.g., multiple registered MRI slice images (including, e.g.,MRI image 10) and/or corresponding MRI parameters obtained from variousequipment, machines, or devices or from a defined time-point (e.g.,specific date) of time range (e.g., within five days after treatment).Each of the MRI parameters in the subject's registered imaging datasetrequires alignment or registration. The registration can be done by, forexamples, using unique anatomical marks, structures, tissues, geometry,and/or shapes or using mathematical algorithms and computer patternrecognition. The values C_(m)

_(n) of the specific imaging parameters for each stop W_(m)

_(n) of the moving window 2, for example, may be obtained from theregistered imaging dataset for the subject.

Referring to FIG. 4, in the step S4 (optional), the reduction of the MRIparameters may be performed using, e.g., subset selection, aggregation,and dimensionality reduction so that a parameter set for each stop ofthe moving window 2 is obtained. The parameter set for each stop W_(m)

_(n) of the moving window 2 may include some of the specific MRIparameters from the step S3 (e.g., T1 mapping, T2 mapping, delta Ktrans,tau, Dt IVIM, fp IVIM, and R*) and values of average Ktrans (obtained byaveraging Ktrans from TM, Ktrans from ETM, and Ktrans from SSM) andaverage Ve (obtained by averaging Ve from TM and Ve from SSM), T2 rawsignal, ADC (high b-values), and nADC (high b-values) are not selectedinto the parameter set because the three MRI parameters are notdetermined to be conditionally independent. T1 mapping, T2 mapping,delta Ktrans, tau, Dt IVIM, fp IVIM, and R* are selected into theparameter set because the seven MRI parameters are determined to beconditionally independent. Performing the step S4 may reduce parameternoise, create new parameter, and assure conditional independence neededfor (Bayesian) classification described in the step S5. A value set mayinclude values for various parameters in the parameter set

In the step S5, in the learning operation (E_(l)), the value set C_(m)

_(n) for each stop W_(m)

_(n) of the moving window 2 from the step S4 (or the values C_(m)

_(n) of some or all of the specific MRI parameters for each stop W_(m)

_(n) of the moving window 2 from the step S3) may be matched to abiomarker library or the classifier CF for an event (e.g., the firstdata type or feature depicted in the section of “description ofclassifier CF”, or biopsy-diagnosed tissue characteristic for, e.g.,specific cancerous cells or occurrence of prostate or breast cancer)created based on data associated with the event from the subset dataDB-1. Accordingly, a probability PW or CL_(m)

_(n) of the event for each stop W_(m)

_(n) of the moving window 2 is obtained. In other words, the probabilityPW or CL_(m)

_(n) of the event for each stop W_(m)

_(n) of the moving window 2 may be obtained based on the value set C_(m)

_(n) (from the step S4) containing the values C_(m)

_(n) of some or all of the specific MRI parameters (from the step S3)for said each stop W_(m)

_(n), of the moving window 2 to match a matching dataset from theestablished or constructed biomarker library or classifier CF. Thebiomarker library or classifier CF, for example, may containpopulation-based information of MRI imaging data and other informationsuch as clinical and demographic data for the event. In the invention,the probability PW or CL_(m)

_(n) of the event for each stop W_(m)

_(n) of the moving window 2 is assumed to be that for the square 4inscribed in said each stop W_(m)

_(n) of the moving window 2.

In the step S6, an algorithm including steps S11 through S16 depicted inFIG. 8 is performed based on the probabilities PWs or CL_(m)

_(n) of the event for the stops W_(m)

_(n) of the moving window 2 to compute probabilities PVs or dl_(k)

_(l) of the event for the respective computation pixels P_(k)

_(l), and the probabilities PVs or dl_(k)-l of the event for therespective computation pixels P_(k)

_(l) form the probability map. The probability map may be obtained in ashort time (such as 10 minutes or 1 hour) after the MRI slice 10obtained. To illustrate the algorithm, the moving window 2 may bedefined to include at least four squares 6, as shown in FIG. 3A, 3B or3C. Each of the squares 6 within the moving window 2, for example, mayhave an area less than 25% of that of the moving window 2. Iwoneighboring stops W_(m)

_(n) of the moving window 2, for example, may have an overlapped regionwith an area A′_(m)

_(n) ranging from 20% to 99% of the area A_(m)

_(u) of any one of the two neighboring stops of the moving window 2, andsome of the squares 6 inside each of the two neighboring stops W_(m)

_(n) of the moving window 2 may be within the overlapped region of thetwo neighboring stops W_(m)

_(n) of the moving window 2. Alternatively, two neighboring stops W_(m)

_(n) of the moving window 2 may have an overlapped region with an areaA′_(m)

_(n) ranging from 1% to 20% of be area A_(m)

_(n) of any one of the two neighboring stops W_(m)

_(n) of the moving window 2. Referring to FIG. 8, in the step S11, theprobability PV or dl_(k)

_(l) of the event for each of the computation pixels P_(k)

_(l) is assumed by, e.g., averaging the probabilities PWs or CL_(m)

_(n) of the event for some of the stops W_(m)

_(n) of the moving window 2, each having one of the squares 6overlapping or covering said each of the computation pixels P_(k)

_(l). The averaging can be arithmetic averaging, Gaussian weightedaveraging or linear regression. In the arithmetic averaging, theprobabilities PWs or CL_(m)

_(n) of the event for the stops of the moving window 2 overlapping orcovering said each of the computation voxels are assumed uniform withinthe stops of moving window 2. In the Gaussian weighted averaging, theprobabilities PWs or CL_(m)

_(n) of the event for the stops of the moving window 2 overlapping orcovering said each of the computation voxels are assumed to be Gaussiandistributed within the stops of moving window 2. In the linearregression method, the probabilities PWs or CL_(m)

_(n) of the event for the stops of the moving window 2 overlapping orcovering said each of the computation voxels are used in a 2D linearregression calculation to obtain the probability of said each of thecomputation voxels.

In the step S12, a probability guess PG for each stop W_(m)

_(n) of the moving window 2 is calculated by, e.g., averaging theprobabilities PVs of the event for all the computation pixels P_(k)

_(l) inside said each stop W_(m)

_(n) of the moving widow 2. In the step S13, a difference DW between theprobability guess PG and the probability PW of the event for each stopW_(m)

_(n) of the moving window 2 is calculated by, e.g., subtracting theprobability PW of the event for said each stop W_(m)

_(n) of the moving window 2 from the probability guess PG for said eachstop W_(m)

_(n) of the moving window 2.

In the step S14, an absolute value of the difference DW between theprobability guess PG and the probability PW of the event for each stopW_(m)

_(n) of the moving window 2 is compared with a preset threshold error orvalue (e.g., 0.001 or 0.0001) to determine whether an error, i.e., theabsolute value of the difference DW, between the probability guess PGand the probability PW of the event for each stop W_(m)

_(n) of the moving window 2 is less than or equal to the presetthreshold error or value. if the absolute value of the difference DW foreach stop W_(m)

_(n) of the moving window 2 is determined in the step S14 to be lessthan or equal to the preset threshold error or value, the step S16continues. In the step S16, the probabilities PVs or dl_(k)

_(l), of the event for the computation pixels P_(k)

_(l) are determined to be optimal, which are called optimalprobabilities hereafter, and the optimal probabilities dl_(k)

_(l) of the respective computation pixels P_(k)

_(l) form the probability map of the event for the MRI image 10 for thesubject having imaging information (e.g., MRI imaging information).After the optimal probabilities, dl_(k)

_(l) for the respective computation pixels P_(k)

_(l) are obtained in the step S16, the algorithm is completed.

If any one of the absolute values of the differences DWs for all thestops W_(m)

_(n), of the moving window 2 is determined in the step S14 to be greaterthan the preset threshold error or value, the step S15 continues. In thestep S15. the probability PV or dl_(k)

_(l), of the event for each of the computation pixels P_(k)

_(l) is updated or adjusted by, e.g., subtracting an error correctionfactor ECF for said each of the computation pixels P_(k)

_(l) from the probability PV or dl_(k)

_(l), of the event for said each of the computation pixels P_(k)

_(l). The error correction factor ECF for each of the computation pixelsP_(k)

_(l) is calculated by, e.g., summing error correction contributions fromthe stops W_(m)

_(n) of the moving window 2 each having one of its squares 6 covering oroverlapping said each of the computation pixels P_(k)

_(l); each of the error correction contributions to said each of thecomputation pixels P_(k)

_(l), for example, may be calculated by multiplying the difference DWfor a corresponding one of the stops W_(m)

_(n) of the moving window 2 by an area ratio of an overlapped areabetween said each of the computation pixels P_(k)

_(l) and the corresponding one of the stops W_(m)

_(n) of the moving window 2 to an area of the square 4 inscribed in thecorresponding one of the stops W_(m)

_(n) of the moving window 2. Alternatively, the error correction factorECF for each of the computation pixels P_(k)

_(l) is calculated by, e.g., dividing the sum of the differences DWs foroverlapping ones of the stops W_(m)

_(n) of the moving window 2, each having one of its squares 6 coveringor overlapping said each of the computation pixels P_(k)

_(l), by the number of all the squares 6 within the moving window 2.After the probabilities PVs or dl_(k)

_(l), of the event for the computation pixels P_(k)

_(l) are updated, the steps S12-S15 are performed repeatedly based onthe updated probabilities PVs or dl_(k)

_(l), of the event for the computation pixels P_(k)

_(l) in the step S15, until the absolute value of the difference DWbetween the probability guess PG and the probability PW or CL_(m)

_(n), of the event for each stop W_(m)

_(n) of the moving window 2 is determined in the step S14 to be lessthan or equal to the preset threshold error or value.

The steps S12-S14 depicted in FIG. 8 may be performed N times, where Nis a positive integer, e.g., greater than 2, 5 or 10. In the first time,the steps S12-S14 are considered to perform the aforementioned stepsST2-ST4, respectively, in this case, the step S11 is considered toperform the aforementioned step ST1. In the second time, the stepsS12-S14 are considered to perform the aforementioned steps ST7-ST9,respectively, in this case, the step S15 is considered to perform theaforementioned steps ST5 and ST6. In the third through N times, thesteps S12-S14, as well as the step S15, are considered to perform theaforementioned step ST10. In addition, the step S16 is considered toperform the aforementioned step ST11.

For detailed description of the steps S11-S16, the square 4 inscribed inthe moving window 2 with the radius Rm is divided into, e.g., nine smallsquares 6 each having width Wsq as shown in FIG. 3B, and in the step S2,the computation region 12 for the probability map is defined with, e.g.,36 computation pixels P_(k)

_(l), i.e., P₁₋₁-P₆₋₆, as shown in FIG. 9 based on the width Wsq of thenine small squares 6 in the moving window 2. Each of the 36 computationpixels P_(k)

_(l), i.e., P₁₋₁-P₆₋₆, used to compose the probability map is defined asa square with the width Wsq. Next, referring to FIGS. 10B, 10D, 10F,10H, 11B, 11D, 11F, 11H, 12B, 12D, 12F, 12H, 13B, 13D, 13F, and 13H, themoving window 2 moves across the computation region 12 at a regular stepor interval X_(fp) and Y_(fp) of a fixed distance in the x and ydirections, and values C_(m)

_(n), i.e., C₁₋₁, C₂₋₁, C₃₋₁, C₄₋₁, C₁₋₂, C_(2-2, C) ₃₋₂, C₄₋₂, C₁₋₃,C₂₋₃C₃₋₃, C₄₋₄C₁₋₄, C₂₋₄, C₃₋₄, and C₄₋₄, of the specific MRI parametersfor sixteen stops i.e., W_(m)

_(n), i.e., W₁₋₁, W₂₋₁, W₃₋₁, W₄₋₁, W₁₋₂W₂₋₂, W₃₋₂, W₄₋₂, W₁₋₃, W₂₋₃,W₃₋₃, W₄₋₃, W₁₋₄, W₂₋₄, W₃₋₄, and W₄₋₄, of the moving window 2 areobtained from the MRI image 10 or the registered imaging dataset. In theexample, the fixed distance X_(fp) and Y_(fp) is substantially equal tothe width Wsq.

Referring to FIGS. 10A and 10B, nine small squares W1 through W9, i.e.,the nine squares 6, within the square 4 inscribed in the stops W₁₋₁ ofthe moving window 2 overlap or cover the nine computation pixels P₁₋₁,P₂₋₁, P₃₋₁, P₁₋₂, P₂₋₂, P₃₋₂, P₁₋₄, P₂₋₄ and P₃₋₄, respectively, andeach of the squares W1-W9 may have an area less than 10% of that of thestop W₁₋₁ of the moving window 2. For details about the squares W1-W9,please refer to the squares 6 illustrated in FIG. 3B. Referring to FIGS.10C and 10D, nine small squares W10 through W18, i.e., the nine squares6, within the square 4 inscribed in the stop W₂₋₁ of the moving window 2overlap or cover the nine computation pixels P₂₋₁, P₃₋₁, P₄₋₁, P₂₋₂,P₃₋₂, P₄₋₂, P₂₋₃, P₃₋₃and P₄₋₃, and respectively, and each of thesquares W10-W18 may have an area less than 10% of that of the stop W₂₋₁of the moving window 2. For details about the squares W10-W18, pleaserefer to the squares 6 illustrated in FIG. 3B. Referring to FIGS. 10Eand 10F, nine small squares W19 through W27, i.e., the nine squares 6,within the square 4 inscribed in the stop W₃₋₁ of the moving window 2overlap or cover the nine computation pixels P₃₋₁, P₄₋₁, P₃₋₁, P₃₋₂,P₄₋₂, P₅₋₂, P₃₋₃, P₄₋₃ and P₅₋₃, respectively, and each of the squaresW19-W27 may have an area less than 10% of that of the stop W₃₋₁ of themoving window 2. For details about the squares W19-W27, please refer tothe squares 6 illustrated in FIG. 3B. Referring to FIGS. 10G and 10H,nine small squares W28 through W36, i.e., the nine squares 6, within thesquare 4 inscribed in the stop W₄₋₁ of the moving window 2 overlap orcover the nine computation pixels P₄₋₁, P₅₋₁, P₆₋₁, P₄₋₂, P₅₋₂, P₆₋₂,P₄₋₃, P₅₋₃, and P₆₋₃, respectively, and each of the squares W28-W36 mayhave an area less than 10% of that of the stop W₄₋₁ of the moving window2. For details about the squares W28-W36, please refer to the squares 6illustrated in FIG. 3B.

Referring to FIGS. 11A and 11B, nine small squares W37 through W45,i.e., the nine squares 6, within the square 4 inscribed in the stop W₁₋₂of the moving window 2 overlap or cover the nine computation pixelsP₁₋₂, P₂₋₂, P₃₋₂, P₁₋₃, P₂₋₃, P₃₋₃, P₁₋₄, P₂₋₄ and P₃₋₄, respectively,and each of the squares W37-W45 may have an area less than 10% of thatof the stop W₁₋₂ of the moving window 2. For details about the squaresW37-W45, please refer to the squares 6 illustrated in FIG. 3B. Referringto FIGS. 11C and 11D, nine small squares W46 through W54, i.e., the ninesquares 6, within the square 4 inscribed in the stop W₂₋₂ of the movingwindow 2 overlap or cover the nine computation pixels P₂₋₂, P₃₋₂, P₄₋₂,P₂₋₃, P₃₋₃, P₄₋₃, P₂₋₄, P₃₋₄ respectively, and each of the squaresW46-W54 may have an area less than 10% of that of the stop W₂₋₂ of themoving window 2. For details about the squares W46-W54, please refer tothe squares 6 illustrated in 3B. Referring to FIGS. 11E and 11F, ninesmall squares W55 through W63, i.e., the nine squares 6, within thesquare 4 inscribed in the stop W₁₋₂ of the moving window 2 overlap orcover the nine computation pixels P₃₋₂, P₄₋₂, P₅₋₂, P₃₋₃, P₄₋₃, P₅₋₃,P₃₋₄, P₄₋₄ and P₅₋₄, and respectively, and each of the squares W55-W63may have an area less than 10% of that of the stop W₃₋₂ of the movingwindow 2. For details about the squares W55-W63, please refer to thesquares 6 illustrated in FIG. 3B. Referring to FIGS. 11G and 11H, ninesmall squares W64 through W72, i.e., the nine squares 6, within thesquare 4 inscribed in the stop W₄₋₂ of the moving window 2 overlap orcover the nine computation pixels P₄₋₂, P₅₋₂, P₆₋₂, P₄₋₃, P₅₋₃, P₆₋₃,P₄₋₄, P₅₋₄and P₆₋₄, respectively, and each of the squares W64-W72 mayhave an area less than 10% of that of the stop W₄₋₂ of the movingwindows 2. For details about the squares W64-W72, please refer to thesquares 6 illustrated in FIG. 3B.

Referring to FIGS. 12A and 12B, nine small squares W73 through W81,i.e., the nine squares 6, within the square 4 inscribed in the stop W₁₋₃of the moving window 2 overlap or cover the nine computation pixelsP₁₋₃, P₂₋₃, P₃₋₃, P₁₋₄, P₂₋₄, P₃₋₄, P_(1-5, P) ₂₋₅ and P₃₋₅,respectively, and each of the squares W71-W81 may have an area less than10% of that of the stop W₁₋₃ of the moving window 2. For details aboutthe squares W73-W81, please refer to the squares 6 illustrated in FIG.3B. Referring to FIGS. 12C and 12D, nine small squares W82 through W90,i.e., the nine squares 6, within the square 4 inscribed in the stop W₂₋₃of the moving window 2 overlap or cover the nine computation pixelsP₂₋₃, P₃₋₃, P₄₋₃, P₂₋₄, P₃₋₄, P₄₋₄, P₂₋₅, P₃₋₅and P₄₋₅, respectively andeach of the squares W82-W90 may have an area less than 10% of that ofthe stop W₂₋₃ of the moving window 2. For details about the squaresW82-W90, please refer to the squares 6 illustrated in FIG. 3B. Referringto FIGS. 12E and 12F, nine small squares W91 through W99, i.e., the ninesquares 6, within the square 4 inscribed in the stop W₃₋₃ of the movingwindow 2 overlap or cover the nine computation pixels P₃₋₃, P₄₋₃, P₅₋₃,P₃₋₄, P₄₋₄, P₅₋₄, P₃₋₅, P₄₋₅ and P₅₋₅, respectively, and each of thesquares W91-W99 may have an area less than 10% of that of the stop W₃₋₃of the moving window 2. For details about the squares W91-W99, pleaserefer to the squares 6 illustrated in FIG. 3B. Referring to FIGS. 12Gand 12H, nine small squares W100 through W108, i.e., the nine squares 6within the square 4 inscribed in the stop of the W₄₋₃ of the movingwindow 2 overlap or cover the nine computation pixels P₄₋₃, P₅₋₃, P₆₋₃,P₄₋₄, P₅₋₄, P₆₋₄, P₄₋₅, P₅₋₅ and P₆₋₅, respectively, and each of thesquares W100-W108 may have an area less than 10% of that of the stopW₄₋₃ of the moving window 2. For details about the squares W100-W108,please refer to the squares 6 illustrated in FIG. 3B.

Referring to FIGS. 13A and 13B, nine small squares W109 through W117,i.e., the nine squares 6, within the square 4 inscribed in the stop W₁₋₄of the moving window 2 overlap or cover the nine computation pixelsP₁₋₄, P₂₋₄, P₃₋₄, P₁₋₅, P₂₋₅, P₃₋₅, P₁₋₆, P₂₋₆ and P₃₋₆ respectively,and each of the squares W109-W117 may have an area less than 10% of thatof the stop W₁₋₄ of the moving window 2. For details about the squaresW109-W117, please refer to the squares illustrated in FIG. 3B. Referringto FIGS. 13C and 13D, nine small squares W118 through W126. i.e., thenine squares 6, within the square 4 inscribed in the stop W₂₋₄ of themoving window 2 overlap or cover the nine computation pixels P₂₋₄, P₃₋₄,P₄₋₄, P₂₋₅, P₃₋₅, P₄₋₅, P₂₋₆, P₃₋₆ and P₄₋₆, respectively, and each ofthe squares W118-W126 may have an area less than 10% of that of the stopW₂₋₄ of the moving window 2. For details about the squares W118-W126,please refer to the squares 6 illustrated in FIG. 3B. Referring to FIGS.13E and 13F, nine small squaws W127 through W135, i.e., the nine squares6, within the square 4 inscribed in the stop W₃₋₄ of the moving window 2overlap or cover the nine computation pixels P₃₋₄, P₄₋₄, P₅₋₄, P₃₋₅,P₄₋₅, P₅₋₅, P₃₋₆, P₄₋₆ and P₅₋₆, respectively, and each of the squaresW127-W135 may have an area less than 10% of that of the stop W₃₋₁ of themoving window 2. For details about the squares W127-W135, please referto the squares 6 illustrated to FIG. 3B. Referring to FIGS. 13G and 16H,nine small squaws W136 through W144, i.e., the nine squares 6, withinthe square 4 inscribed in the stop W₄₋₄ of the moving window 2 overlapor cover the nine computation pixels P₄₋₄, P₅₋₄, P₆₋₄, P₄₋₅, P₅₋₅, P₆₋₅,P₄₋₆, P₅₋₆ and P₆₋₆, respectively, and each of the squares W136-W144 mayhave an area less than 10% of that of the stop W₄₋₄ of the moving window2. For details about the squares W136-W144, please refer to the squares6 illustrated in FIG. 3B.

After the values C_(m)

_(n) i.e., C₁₋₁-C₄₋₄, of the specific MRI parameters for the sixteenstops W_(m)

_(n) i.e., W₁₋₁-W₄₋₄, of the moving window 2 are obtained, the step S5is performed for engineering learning or machine learning to obtain theprobabilities PWs or CL_(m)

_(n), i.e., CL₁₋₁-CL₄₋₄, of the event for the respective stops W_(m)

_(n), i.e., W₁₋₁-W₄₋₄, of the moving window 2. The probabilities PWs orCL_(m)

_(n), i.e., CL₁₋₁, CL₂₋₁, CL₃₋₁, CL₄₋₁, CL₁₋₂, CL₂₋₂, CL₃₋₂, CL₄₋₂,CL₁₋₃, CL₂₋₃, CL₃₋₃, CL₄₋₃, CL₁₋₄, CL₂₋₄, CL₃₋₄, and CL₄₋₄, of the eventfor the sixteen stops W₁₋₁, W₂₋₁, W₃₋₁, W₄₋₁, W₁₋₂, W₂₋₂, W₃₋₂, W₄₋₂,W₁₋₃, W₂₋₃, W₃₋₃, W₄₋₃, W₁₋₄, W₂₋₄, W₃₋₄, and W₄₋₄of the moving window2, for example, are assumed to be 0.6055, 0.5628, 0.5366, 0.4361,0.4982, 0.5534, 0.5521, 0.4227, 0.4618, 0.5132, 0.6214, 0.5810, 0.4371,0.4698, 0.5774, and 0.5613, respectively. In the example, the sixteenprobabilities PWs or CL_(m)

_(n), i.e., CL₁₋₁-CL₄₋₄, of the event for the sixteen stops W_(m)

_(n), i.e., W₁₋₁-W₄₋₄, of the moving window 2 are assumed to be thosefor the sixteen squares 4 inscribed In the respective stops W_(m)

_(n), i.e., W₁₋₁-W₄₋₄, of the moving window 2, respectively. In otherwords, the sixteen probabilities of the event for the sixteen squares 4inscribed in the sixteen stops W_(m)

_(n), i.e., W₁₋₁-W₄₋₄, of the moving window 2 are 0.6055, 0.5628,0.5366, 0.4361, 0.4982, 0.5534, 0.5521, 0.4227, 0.4618, 0.5132, 0.6214,0.5810, 0.4371, 0.4698, 0.5774, and 0.5613, respectively.

Next, the algorithm depicted in FIG. 8 is performed based on theprobabilities PWs or CL_(m)

_(n), i.e., CL₁₋₁-CL₄₋₄, of the event for the sixteen stops W_(m)

_(n), i.e., W₁₋₁-W₄₋₄, of the moving window 2 to obtain or calculateoptimal probabilities PVs or dl_(k)

_(l), i.e., dk₁₋₁-dk₆₋₆, of the event for the computation pixels P_(k)

_(l), i.e., P₁₋₁-P₆₋₆, as described in the following specification.First of all, the probabilities PVs or dl_(k)

_(l), i.e., dk₁₋₁-dk₆₋₆, of the event for the computation pixels P_(k)

_(l), i.e., P₁₋₁-P₆₋₆, as shown in FIG. 14A are assumed by the step S11.In the step S11, referring to FIGS. 10A-10H, 11A-11H, 12A-12H, 13A-13H,and 14A, because the only stop W₁₋₁ of the moving window 2 has thesquare W1 overlapping the computation pixel P₁₋₁, the probability PV,i.e., dl₁₋₁, of the event for the computation pixel P₁₋₁ is assumed tobe the probability PW, CL₁₋₁ equal to 0.6055, of the event for the stopW₁₋₁ of the moving window 2. Similarly, the probabilities PVs, i.e.,dl₆₋₁, dl₁₋₆ and dl₆₋₆, of the event for the computation pixels P₆₋₁,P₁₋₆ and P₆₋₆ are assumed to be the probabilities PWs, i.e., CL₆₋₁,CL₁₋₆, and CL₆₋₆ equal to 0.4361, 0.4371 and 0.5613 respectively, of theevent for the stops W₄₋₁, W₁₋₄, and W₄₋₁ of the moving window 2,respectively.

Because the only two stops W₁₋₁ and W₂₋₁ of the moving window 2 have thesquares W2 and W10 overlapping the computation pixel P₂₋₁, theprobability PV, i.e., dl₂₋₁, of the event for the computation pixel P₂₋₁is assumed to be the average, i.e., 0.5841, of the two probabilitiesPWs, CL₁₋₁ and CL₂₋₁ equal to 0.6055 and 0.5628 respectively, of theevent for the stops W₁₋₁ and W₂₋₁ of the moving window 2. Similarly, theprobability PV, i.e., dl₅₋₁, of the event for the computation pixel P₅₋₁is assumed to be the average, i.e., 0.4863, of the probabilities PWs,i.e., CL₃₋₁ and CL₄₋₁ equal to 0.5366 and 0.4361 respectively, of theevent for the stops W₃₋₁ and W₄₋₁ of the moving window 2. Theprobability PV, i.e., dl₁₋₂, of the event for the computation pixel P₁₋₂is assumed to be the average, i.e., 0.5519, of the probabilities PWs,i.e., CL₁₋₁ and CL₁₋₂ equal to 0.6055 and 0.4982 respectively, of theevent for the stops and W₁₋₁ and W₁₋₂ of the moving window 2. Theprobability PV, i.e., dl₆₋₂ of the event for the computation pixel P₆₋₂is assumed to be the average, i.e, 0.4294, of the probabilities PWs,i.e., CL₁₋₁ and CL₁₋₂ equal to 0.4361 and 0.4227 respectively, of theevent for the stops W₁₋₁ and W₁₋₂ of the moving window 2. Theprobability PV, i.e., dl₁₋₅ of the event for the computation pixel P₁₋₅is assumed to be the average, i.e., 0.4495, of the probabilities PWs,i.e., CL₁₋₃ and CL₁₋₄ equal to 0.4618 and 0.4371 respectively, of theevent for the stops W₁₋₃ and W₁₋₄ of the moving window 2. theprobability PV, i.e., dl₆₋₅, of the event for the computation pixel P₆₋₅is assumed to be the average, i.e., 0.5711, of the probabilities PWs,i.e., CL₄₋₃ and CL₄₋₄ equal to 0.5810 and 0.5613 respectively, of theevent for the stops W₄₋₁ and W₄₋₄ of the moving window 2. Theprobability PV, i.e., dl₂₋₆, of the event for the computation pixel P₂₋₆is assumed to be the average, i.e., 0.4535, of the probabilities PWs,i.e., CL₁₋₄ and CL₂₋₄ equal to 0.4371 and 0.4698 respectively, of theevent for the stops W₁₋₄ and P₂₋₄ of the moving window 2. Theprobability PV, i.e dl₅₋₆, of the event for the computation pixel P₅₋₆is assumed to be the average, i.e., 0.5693, of the probabilities PWs,i.e., CL₁₋₁ and CL₁₋₄ equal to 0.5774 and 0.5613 respectively, of theevent for the stops W₃₋₄ and W₄₋₄ of the moving window 2.

Because the only three stops W₁₋₁ , W₂₋₁ and W₃₋₁ of the moving window 2have the squares W3, W11 and W19 overlapping the computation pixel P₃₋₁,the probability PV, i.e., dl₃₋₁, of the event for the computation pixelP₃₋₁ is assumed to be the average, i.e., 0.5683, of the threeprobabilities PWs, i.e., CL₁₋₁, CL₂₋₁ and CL₃₋₁ equal to 0.6055, 0.5628and 0.5366 respectively, of the event for the stops W₁₋₁, W₂₋₁ and W₃₋₁of the moving window 2. Similarly, the probability PV, i.e., dl₄₋₁, ofthe event for the computation pixel P₄₋₁ is assumed to be the average,i.e., 0.5118, of the probabilities PWs, i.e., CL₂₋₁, CL₃₋₁ and CL₄₋₁, ofthe event for the stops W₂₋₁, W₃₋₁ and W₄₋₁ of the moving window 2. Theprobability PV, i.e., dl₁₋₃ of the event for the computation pixel P₁₋₃is assumed to be the average, i.e., 0.5219, of the probabilities PWs,i.e., CL₁₋₁, CL₁₋₂ and CL₁₋₃, of the event for the stops W₁₋₁, W₁₋₂ andW₁₋₃ of the moving window 2. The probability PV, i.e., dl₆₋₁, of theevent for the computation pixel P₆₋₃ is assumed to be the average, i.e.,0.4799, of the probabilities PWs, i.e., CL₄₋₁, CL₄₋₂ and CL₄₋₃, of theevent for the stops W₄₋₁, W₄₋₂ and W₄₋₃ of the moving window 2. Theprobability PV, i.e., dl

, of the event for the computation pixel P₁₋₁ is assumed to be theaverage, i.e., 0.4657, of the probabilities PWs, i.e., CL₁₋₂, CL₁₋₃ andCL₁₋₄, of the event for the stops W₁₋₂, W₁₋₃ and W₁₋₄ of the movingwindow 2. The probability PV, i.e., dl₆₋₁, of the event for thecomputation pixel P₆₋₁ is assumed to be the average, i.e., 0.5216, ofthe probabilities PWs, i.e., CL₁₋₂, CL₁₋₃ and CL₁₋₄, of the event forthe stops W₄₋₂, W₄₋₃ and W₄₋₄ of the moving window 2. The probabilityPV, i.e., dl₃₋₆, of the event for the computation pixel P₃₋₆ is assumedto be the average, i e., 0.4948, of the probabilities PWs, i.e., CL₁₋₄,CL₂₋₄ and CL₃₋₄, of the event for the stops W₁₋₄, W₂₋₄ and W₃₋₄ of themoving window 2. The probability PV, i.e., dl₄₋₆, of the event for thecomputation pixel P₄₋₆ is assumed to be the average, i.e., 0.5362, ofthe probabilities PWs, i.e., CL₂₋₄, CL₃₋₄ and CL₄₋₄, of the event forthe stops W₂₋₄. W₃₋₄ and W₄₋₄ of the moving window 2

Because the only four stops W₁₋₁, W₂₋₁, W₁₋₂ and W₂₋₂ of the movingwindow 2 have the squares W5, W13, W38 and W46 overlapping thecomputation pixel P₂₋₂, the probability PV, i.e., dl₂₋₂, of the eventfor the computation pixel P₂₋₂ is assumed to be the average, i.e.,0.5550, of the four probabilities PWs, i.e., CL₁₋₁, CL₂₋₁ CL₁₋₂ andCL₂₋₂ equal to 0.6055, 0.5628, 0.4982 and 0.5534 respectively, of theevent an the stops W₁₋₁, W₂₋₁, W₁₋₂ and W₂₋₂ of the moving window 2.Similarly, the probability PV, i.e., dl₅₋₂, of the event for thecomputation pixel P₅₋₂ is assumed to be the average, i.e., 0.4869, ofthe probabilities PWs, i.e., CL₃₋₁, CL₄₋₁ CL₃₋₂ and CL₄₋₂, of the eventfor the stops W₃₋₁, W₄₋₁, W₃₋₂ and W₄₋₂ of the moving window 2. Theprobability PV, i.e., dl₂₋₅, of the event the computation pixel P₂₋₅ isassumed to be the average, i.e., 0.4705, of the probabilities PWs, i.e.,CL₁₋₃, CL₂₋₃ CL₁₋₄ and CL₂₋₄, of the event for the stops W₁₋₃, W₂₋₃,W₁₋₄ and W₂₋₄ of the moving window 2. The probability PV, i.e., dl₅₋₅,of the event for the computation pixel P₅₋₅ is assumed to be theaverage, i.e., 0.5852, of the probabilities PWs, i.e., CL₃₋₃, CL₄₋₄CL₃₋₄ and CL₄₋₄ of the event for the stops W₃₋₃, W₄₋₃, W₃₋₃ and W₄₋₄ ofthe moving window 2.

Because the only six stops W₁₋₁, W₂₋₁, W₃₋₁, W₁₋₂, W₂₋₂ , and W₃₋₂ ofthe moving window 2 have the squares W6, W14, W22, W39, W47 and W55overlapping the computation pixel P₃₋₂, the probability PV, i.e., dl₃₋₂,of the event for the computation pixel P₃₋₂ is assumed to be theaverage, i.e., 0.5514, of the six probabilities PWs, i.e., CL₁₋₁, CL₂₋₁,CL₃₋₁, CL₁₋₂, CL₂₋₂ and CL₃₋₂ equal to 0.6055, 0.5628, 0.5366, 0.4982,0.5534 and 0.5521 respectively, of the event for the stops W₁₋₁, W₂₋₁,W₃₋₁, W₁₋₂, W₂₋₂ and W₃₋₂ of the moving window 2. Similarly, theprobability PV, i.e., dl₄₋₂, of the event for the computation pixel P₄₋₂is assumed to be the average, i.e., 0.5106, of the probabilities PWs,i.e., CL₂₋₄, CL₃₋₄, CL₄₋₄, CL₂₋₂, CL₃₋₂ and CL₄₋₂, of the event for thestops W₂₋₁, W₂₋₁, W₄₋₁, W₂₋₂, W₃₋₂ and W₄₋₂ of the moving window 2. Theprobability PV, i.e., dl₂₋₃, of the event fiat the computation pixelP₂₋₃ is assumed to be the average, i.e., 0.5325, of the probabilitiesPWs, i.e., CL₁₋₁, CL₂₋₁, CL₁₋₂, CL₂₋₂, CL₁₋₃ and CL₂₋₃, of the event furthe stops W₁₋₁, W₂₋₁, W₁₋₂, W₂₋₂, W₁₋₃ and W₂₋₃ of the moving window 2.The probability PV, i.e., dl₅₋₃, of the event for the computation pixelP₅₋₃ is assumed to be the average, i.e., 0.5250, of the probabilitiesPWs, i.e., CL₃₋₁, CL₄₋₁, CL₃₋₂, CL₄₋₂, CL₃₋₃ and CL₄₋₃, of the event forthe stops W₃₋₁, W₄₋₁, W₃₋₂, W₄₋₂, W₃₋₃ and W₄₋₃ of the moving window 2.The probability PV, i.e., dl₂₋₄, of the event for the computation pixelP₂₋₄ is assumed to be the average, i.e., 0.4889, of the probabilitiesPWs, i.e., CL₁₋₂, CL₂₋₂, CL₁₋₃, CL₂₋₃, CL₁₋₄ and CL₂₋₄, of the event forthe stops W₁₋₂, W₂₋₂, P₁₋₃, W₂₋₃, W₁₋₄ and W₂₋₄ of the moving window 2.The probability PV, i.e., dl₅₋₄, of the event for the computation pixelP₅₋₄ is assumed to be the average, i.e., 0.5526, of the probabilitiesPWs, i.e., CL₃₋₂, CL₄₋₂, CL₃₋₃, CL₄₋₃, CL₃₋₄ and CL₄₋₄, of the event forthe stops W₃₋₂, W₄₋₂, W₃₋₃, W₄₋₃, W₃₋₄ and W₄₋₄ of the moving window 2.The probability PV, i.e., dl₃₋₅, of the event for the computation pixelP₃₋₅ is assumed to be the average, i.e., 0.5134, of the probabilitiesPWs, i.e., CL₁₋₃, CL₂₋₃, CL₃₋₃, CL₁₋₄, CL₂₋₄ and CL₃₋₄, of the event forthe stops W₁₋₃, W₂₋₃, W₃₋₃, W₁₋₄, W₂₋₄ and W₃₋₄ of the moving window 2.The probability PV, i.e., dl₄₋₅, of the event for the computation pixelP₄₋₅ is assumed to be the average, i.e., 0.5540, of the probabilitiesPWs, i.e., CL₂₋₃, CL₃₋₃, CL₃₋₃, CL₂₋₄, CL₃₋₄ and CL₄₋₄, of the event forthe stops W₂₋₃, W₃₋₃, W₄₋₃, W₂₋₄, W₃₋₄ and W₄₋₄ of the moving window 2.

Because the only nine stops W₁₋₁, W₂₋₁, W₃₋₁, W₁₋₂, W₂₋₂, W₃₋₂, W₁₋₃,W₂₋₃ and W₃₋₃ of the moving window 2 have the squares W9, W17, W25, W42,W50, W58, W75, W83 and W91 overlapping the computation pixel P₃₋₃, theprobability PV, i.e., dl₃₋₃, of the event for the computation pixel P₃₋₃is assumed to be the average, i.e., 0.5450, of the nine probabilitiesPWs, i.e., CL₁₋₁, CL₂₋₁, CL₃₋₁, CL₁₋₂, CL₂₋₂, CL₃₋₂, CL₁₋₃, CL₂₋₃ andCL₃₋₃ equal to 0.6055, 0.5628, 0.5366, 0.4982, 0.5534, 0.5521, 0.4618,0.5132 and 0.6214 respectively, of the event for the stops W₁₋₁, W₂₋₁,W₃₋₁, W₂₋₁, W₂₋₂, W₃₋₂, W₁₋₃, W₂₋₃ and W₃₋₃ of the moving window 2.Similarly, the probability PV, i.e., dl₄₋₃, of the event for thecomputation pixel P₄₋₃ is assumed to be the average, i.e., 0.5310, ofthe probabilities PWs, i.e., CL₂₋₄, CL₃₋₄, CL₄₋₄, CL₂₋₂, CL₃₋₂, CL₄₋₂,CL₂₋₃, CL₃₋₃ and CL₄₋₃, of the event for the stops W₂₋₁, W₃₋₁, W₄₋₁,W₂₋₂, W₃₋₂, W₄₋₂, W₂₋₃, W₃₋₃ and W₄₋₃ of the moving window 2. Theprobability PV, i.e., dl₃₋₄, of the event for the computation pixelP₃₋₄, is assumed to be the average, i.e., 0.5205, of the probabilitiesPWs, i.e., CL₁₋₂, CL₂₋₂, CL₃₋₂, CL₁₋₃, CL₂₋₃, CL₃₋₃, CL₁₋₄, CL₂₋₄ andCL₃₋₄, of the event for the stops W₁₋₂, W₂₋₂, W₃₋₂, W₁₋₃, W₂₋₃, W₃₋₃,W₁₋₄, W₂₋₄ and W₃₋₄ of the moving window 2. The probability PV, i.e., dl

, of the event for the computation pixel P

, is assumed to be the average, i.e., 0.5391, of the probabilities PWs,i.e., CL₂₋₂, CL₃₋₂, CL₄₋₂, CL₂₋₃, CL₃₋₃, CL₄₋₃, C₂₋₄, CL₃₋₄ and CL₄₋₄,of the event for the stops W₂₋₂, W₃₋₂, W₄₋₂, W₂₋₃, W₃₋₃, W₄₋₃, W₂₋₄,W₃₋₄ and W₄₋₄ of the moving window 2.

After the probabilities PVs or dl_(k)

_(l), i.e., dl₁₋₁-dl₆₋₆, of the event for the respective computationpixels P_(k)

_(l), i.e., P₁₋₁-P₆₋₆, are assumed, the step S12 is performed to obtainsixteen probability guesses PGs for the respective stops W_(m)

_(n), i.e., W₁₋₁, W₂₋₁, W₃₋₁, W₄₋₁, W₁₋₂, W₂₋₂, W₃₋₂, W₄₋₂, W₁₋₃, W₂₋₃,W₃₋₃, W₄₋₃, W₁₋₄, W₂₋₄, W₃₋₄, and W₄₋₄, of the moving window 2. Theprobability guess PG for each of the sixteen stops W_(m)

_(n), i.e., W₁₋₁-W₄₋₄, of the moving window 2 is calculated by averagingnine of the probabilities PVs or dl_(k)

_(l), i.e., dl₁₋₁-dl₆₋₆, of the event low respective nine of thecomputation pixels P_(k)

_(l), i.e., P₁₋₁-P₆₋₆, overlapping or covering the respective nine smallsquares 6 within the square 4 inserted in said each of the sixteen stopsW₁₋₁-W₄₋₄ of the moving window 2. For example, because the nine smallsquares W1-W9 within the square 4 inscribed in the stop W₁₋₁ of themoving window 2 overlap or cover the respective computation pixels P₁₋₁,P₂₋₁, P₃₋₁, P₁₋₂, P₂₋₂, P₃₋₂, P₁₋₃, P₂₋₃ and P₃₋₃, the probability guessPG for the stop W₁₋₁ of the moving window 2 is calculated by averagingthe nine probabilities PVs, i.e., dl₁₋₁, dl₂₋₁, dl₃₋₁, dl₁₋₂, dl₂₋₂,dl₃₋₂, dl₁₋₃, ₂₋₃ and dl₃₋₃ equal to 0.6055, 0.5841, 0.5683, 0.5519,0.5550, 0.5514, 0.5219, 0.5325 and 0.5450 respectively, of the event forthe computation pixels P₁₋₁, P₂₋₁, P₃₋₁, P₁₋₂, P₂₋₂, P₃₋₂, P₁₋₃, P₂₋₃and P₃₋₃ inside the stop W₁₋₁ of the moving window 2. Accordingly, theprobability guesses PGs for the stops W_(m)

_(n), i.e., W₁₋₁, W₂₋₁, W₃₋₁, W₁₋₁, W₁₋₂, W₂₋₂, W₃₋₂, W₄₋₂, W₁₋₃, W₂₋₃,W₃₋₃, W₄₋₃, W₁₋₄, W₂₋₄, W₃₋₄, and W₄₋₄, of the moving window 2 are0.5573, 0.5433, 0.5240, 0.4886, 0.5259, 0.5305, 0.5291, 0.5085, 0.5009,0.5217, 0.5407, 0.5400, 0.4771, 0.5079, 0.5406, and 0.5545,respectively.

After the sixteen probability guesses PGs are obtained or calculated,the step S13 is performed to obtain sixteen differences DWs for thesixteen stops W_(m)

_(n), i.e., W₁₋₁-W₄₋₄, of the moving window 2. Each of the sixteendifferences DWs is calculated by, e.g., subtracting the probability PWor CL_(m)

_(n) i.e., CL₁₋₁-CL₄₋₄, of the event for a corresponding one of thesixteen stops W_(m)

_(n), i.e., W₁₋₁-W₄₋₄, of the moving window 2 from the probability guessPG for the corresponding one of the sixteen stops W_(m)

_(n)i.e., W₁₋₁-W₄₋₄, of the moving window 2. For example, the differenceDW for the stop W₁₋₁ of the moving window 2 is calculated by subtractingthe probability PW, i.e., CL₁₋₁ equal to 0.6055, of the event for thestop W₁₋₁ of the moving window 2 from the probability guess PG, i.e.,0.5573, for the stop W₁₋₁ of the moving window 2. Accordingly, thedifferences DWs for the stops W_(m)

_(n), i.e., W₁₋₁, W₂₋₁, W₃₋₁, W₄₋₁, W₁₋₂, W₂₋₂, W₃₋₂, W₄₋₂, W₁₋₃, W₂₋₃,W₃₋₃, W₄₋₃, W₁₋₄, W₂₋₃, W₃₋₄, and W₄₋₄, of the moving window 2 are−0.0482, −0.0194, −0.0126, 0.0525, 0.0276, −0.0230, −0.0230, 0.0858,0.0391, 0.0085, −0.0807, −0.0410, 0.0400, 0.0380, −0.0368, and −0.0068,respectively.

After the sixteen differences DWs are obtained or calculated, the stepS14 is performed to determine whether absolute values of the sixteendifferences DWs are less than or equal to a preset threshold value of0.0001. Because the absolute values of the sixteen differences DWs aregreater than the preset threshold value, the step S15 continues in whichthe probabilities PVs or dl_(k)

_(l), i.e., dl₁₋₁-dl₆₋₆, of the event for the computation pixels P_(k)

_(l), i.e., P₁₋₁-P₆₋₆, are updated, as shown in FIG. 14B.

In the step S15, the updated probability PV or dl_(k)

_(l), i.e., updated dl₁₋₁-dl₆₋₆, of the event for each of thecomputation pixels P_(k)

_(l), i.e., P₁₋₁-P₆₋₆, is calculated by, e.g., subtracting an errorcorrection factor ECF for said each of the computation pixels P_(k)

_(l), i.e., P₁₋₁-P₆₋₆, from the current probability PV or dl_(k)

_(l), i.e., current dl₁₋₁-dl₆₋₆, of the event for said each of thecomputation pixels P_(k)

_(l), i.e., P₁₋₁-P₆₋₆. The error correction factor ECF for each of the 4computation pixels P₁₋₁, P₆₋₁, P₁₋₆ and P₆₋₆ is obtained by, e.g.,calculating an error correction contribution only from a correspondingone of the stops W₁₋₁, W₄₋₂, W₁₋₄ and W₄₋₄ of the moving window 2, whichhas one of its squares 6 covering or overlapping said each of the 4computation pixels P₁₋₁, P₆₋₁, P₁₋₆ and P₆₋₆. For example, because theonly stop W₁₋₁ of the moving window 2 has the small square W1 coveringor overlapping the computation pixel P₁₋₁, the error correction factorECF, i.e., −0.0054, for the computation pixel P₁₋₁ is obtained bycalculating the error correction contribution only from the stop W₁₋₁ ofthe moving window 2. The error correction contribution to thecomputation pixel P₁₋₁ from the stop W₁₋₁ of the moving window 2 iscalculated by multiplying the difference DW, i.e., −0.0482, for the stopW₁₋₁ of the moving window 2 by an area ratio, i.e., 1/9, of anoverlapped area between the computation pixel P₁₋₁ and the stop W₁₋₁ ofthe moving window 2 to an area of the square 4 inscribed in the stopW₁₋₁ of the moving window 2. Accordingly, the updated probability PV,i.e., updated dl₁₋₁, of the event for the computation pixel P₁₋₁ iscalculated by subtracting the error correction factor ECF, i.e.,−0.0054, for the computation pixel P₁₋₁ from the current probability PV,i.e., current dl₁₋₁ equal to 0.6055, of the event for the computationpixel P₁₋₁.

The error correction facto ECF for each of the 32 computation pixelsP₂₋₁-P₅₋₁, P₁₋₂-P₆₋₂, P₁₋₃-P₆₋₃, P₁₋₄-P₆₋₄, P₁₋₅-P₆₋₅ and P₂₋₆-P₅₋₆ iscalculated by, e.g., summing error correction contributions fromoverlapping ones of the stops W_(m)

_(n), i.e., W₁₋₁-W₄₋₄, of the moving window 2, each having one of itssquares 6 covering or overlapping said each of the 32 computation pixelsP₂₋₁-P₅₋₁, P₁₋₂-P₆₋₂, P₁₋₃-P₆₋₃, P₁₋₄-P₆₋₄, P₁₋₅-P₆₋₅ and P₂₋₆-P₅₋₆;each of the error correction contributions to said each of the 32computation pixels P₁₋₂-P₅₋₁, P₁₋₂-P₆₋₂, P₁₋₃-P₆₋₃, P₁₋₄-P₆₋₄, P₁₋₅-P₆₋₅and P₂₋₆-P₅₋₆ is calculated by multiplying the difference DW for acorresponding one of the overlapping ones of the stops W_(m)

_(n), i.e., W₁₋₁-W₄₋₄, of the moving window 2 by an area ratio of anoverlapped area between said each of the 32 computation pixelsP₂₋₁-P₅₋₁, P₁₋₂-P₆₋₂, P₁₋₃-P₆₋₃, P₁₋₄-P₆₋₄, P₁₋₅-P₆₋₅ and P₂₋₆-P₅₋₆ andthe corresponding one of the overlapping ones of the stops W_(m)

_(n), i.e., W₁₋₁-W₄₋₄, of the moving window 2 to an area of the square 4inscribed in the corresponding one of the overlapping ones of the stopsW_(m)

_(n), i.e., W₁₋₁-W₄₋₄, of the moving window 2. For example, because theonly nine stops W₁₋₁, W₂₋₁, W₃₋₁, W₁₋₂, W₂₋₂, W₃₋₂, W₁₋₃, W₂₋₃ and W₃₋₃of the moving window 2 have the squares W9, W17, W25, W42, W50, W58,W75, W83 and W91 covering or overlapping the computation pixel P₁₋₃, theerror correction factor ECF, i.e., −0.0146, for the computation pixelP₃₋₃ is obtained by summing error correction contributions from therespective stops W₁₋₁, W₂₋₁, W₃₋₁, W₁₋₂, W₂₋₂, W₃₋₂, W₁₋₃, W₂₋₃, andW₃₋₃ of the moving window 2. The error correction contribution, i.e.,−0.0053, from the stop W₁₋₄ of the moving window 2 to the computationpixel P₃₋₁ is calculated by multiplying the difference DW, i.e.,−0.0482, for the stop W₁₋₁ of the moving window 2 by an area ratio,i.e., 1/9, of an overlapped area between the computation pixel P₁₋₁ andthe stop W₁₋₁ of the moving window 2 to the area of the square 4inscribed in the stop W₁₋₁ of the moving window 2. The error correctioncontribution, i.e., −0.0021, from the stop W₂₋₁ of the moving window 2to the computation pixel P₃₋₃ is calculated by multiplying thedifference DW, i.e., −0.0194, for the stop W₂₋₁ of the moving window 2by an area ratio, i.e., 1/9, of an overlapped area between thecomputation pixel P₃₋₃ and the stop W₂₋₄ of the moving window 2 to thearea of the square 4 inscribed in the stop W₂₋₁ of the moving window 2.The error correction contribution, i.e., −0.0014, from the stop W₃₋₁ ofthe moving window 2 to the computation pixel P₃₋₃ is calculated bymultiplying the difference DW, i.e., −0.0126, for the stop W₃₋₁ of themoving window 2 by an area ratio, i.e., 1/9, of an overlapped areabetween the computation pixel P₃₋₃ and the stop W₃₋₁ of the movingwindow 2 to the area of the square 4 inscribed in the stop W₃₋₁ of themoving window 2. The error correction contribution, i.e., 0.0031, fromthe stop W₁₋₂ of the musing window 2 to the computation pixel P₃₋₃ iscalculated by multiplying the difference DW, i.e., 0.0276, for the stopW₁₋₂ of the moving window 2 by an area ratio, i.e., 1/9, of anoverlapped area between the computation pixel P₃₋₃ and the stop W₁₋₂ ofthe moving window 2 to the area of the square 4 inscribed in the stopW₁₋₂ of the moving window 2. The error correction contribution, i.e.,−0.0026, from the stop W₂₋₂ of the moving window 2 to the computationpixel P₃₋₃ is calculated by multiplying the difference DW, i.e.,−0.0230, for the stop W₂₋₂ of the moving window 2 by an area ratio,i.e., 1/9, of an overlapped area between the computation pixel P₃₋₃ andthe stop W₂₋₂ of the moving window 2 to the area of the square 4inscribed in the stop W₂₋₂ of the moving window 2. The error correctioncontribution, i.e., −0.0026, from the stop W₃₋₂ of the moving window 2to the computation pixel P₃₋₃ is calculated by multiplying thedifference DW, i.e., −0.0230, for the stop W₃₋₂ of the moving window 2by an area ratio, i.e., 1/9, of an overlapped area between thecomputation pixel P₃₋₃ and the stop W₃₋₂ of the moving window 2 to thearea of the square 4 inscribed in the stop W₃₋₂ of the moving window 2.The error correction contribution, i.e., 0.0043, from the stop W₁₋₃ ofthe moving window 2 to the computation pixel P₃₋₃ is calculated bymultiplying the difference DW, i.e., 0.0391, for the stop W₁₋₃ of themoving window 2 by an area ratio, i.e., 1/9, of an overlapped areabetween the computation pixel P₃₋₃ and the stop W₁₋₃ of the movingwindow 2 to the area of the square 4 inscribed in the stop W₁₋₃ of themoving window 2. The error correction contribution, i.e., 0.0009, fromthe stop W₂₋₃ of the moving window 2 to the computation pixel P₃₋₃ iscalculated by multiplying the difference DW, i.e., 0.0085, for the stopW₂₋₃ of the moving window 2 by an area ratio, i.e., 1/9, of anoverlapped area between the computation pixel P₃₋₃ and the stop W₂₋₃ ofthe moving window 2 to the area of the square 4 inscribed in the stopW₂₋₃ of the moving window 2. The error correction contribution, i.e.,−0.0089, from the stop W₃₋₃ of the moving window 2 to the computationpixel P₃₋₃ is calculated by multiplying the difference DW, i.e.,−0.0807, for the stop W₃₋₃ of the moving window 2 by an area ratio,i.e., 1/9, or on overlapped area between the computation pixel P₃₋₃ andthe stop W₃₋₃ of the moving window 2 to the area of the square 4inscribed in the stop W₃₋₃ of the moving window 2. Accordingly, theupdated probability PV, i.e., updated dl₃₋₃, of the event for thecomputation pixel P₃₋₃ is calculated by subtracting the error correctionfactor ECF, i.e., −0.0146, for the computation pixel P₃₋₃ from thecurrent probability PV, i.e., i.e., current dl₃₋₃ is equal to 0.5450, ofthe event for the computation pixel P₃₋₃.

After the updated probabilities PVs or dl_(k)

_(l), i.e., updated dl₁₋₁-dl₆₋₆, of the event for the computation pixelsP_(k)

_(l), i.e., P₁₋₁-P₆₋₆, are obtained or calculated, the steps S12-S15 areperformed repeatedly based on the updated probabilities PVs or dl_(k)

_(l), i.e., updated dl₁₋₁-dl₆₋₆, of the event for the computation pixelsP_(k)

_(l), i.e., P₁₋₁-P₆₋₆, in the step S15, until the absolute values of thesixteen differences DWs for the sixteen stops W_(m)

_(n), i.e., W₁₋₁-W₄₋₄, of the moving window 2 are less than or equal tothe preset threshold value. Accordingly, the optimal probabilities PVsor dl_(k)

_(l), i.e., optimal dl₁₋₁-dl₆₋₆, of the event for the computation pixelP_(k)

_(l), i.e., P₁₋₁-P₆₋₆, as shown in FIG. 14C, are obtained and form theprobability map for the event.

The above process, including the steps S1-S6, is performed to generatethe moving window 2 across the computation regions 12 of the MRI slice10 along the x and y directions to create a two-dimensional (2D)probability map. In order to obtain a three-dimensional (3D) probabilitymap, the above process, including the steps S1-S6, may be applied toeach of all MRI slices (including the MRI slice 10) of the subjectarranged in the z direction perpendicular to the x and y directions.

The invention provides a computing method, i.e., the steps S1-S6, toobtain values of the specific MRI parameters for multiple large regionsor volumes of the MRI image 10 (i.e., the stops of the moving window 2)each covering multiple machine-defined original pixels p_(i)

_(j) of the MRI image 10 and to obtain a probability map having smallregions (i.e., computation pixels P_(k)

_(l)) with extremely accurate probabilities dl_(k)

_(l) based on the values C_(m)

_(n) of the specific MRI parameters for the large regions or volumes(i.e., moving windows W_(m)

_(n)), which overlaps, of the MRI image 10. Because of calculation forthe probabilities CL_(m)

_(n) based on the large regions or volumes (i.e., moving windows W_(m)

_(n)) of the MRI image 10, registered or aligned errors between theregistered image sets (or registered parameter maps) for differentparameters can be compensated.

In the algorithm depicted in FIG. 8, some of the steps S11-S16, forexample, may be performed on one or more MRI machines. In the computingmethod depicted in FIG. 4, the steps S1-S6, for example, may beperformed on a MRI system, which may include one or more MRI machines toperform some or all of the steps S11-S16. A probability map foroccurrence of prostate cancer, for example, may be formed by the MRIsystem to perform the steps S1-S6 and shows a probability of cancer fora small portion of the prostate.

By repeating the stops S1-S6 of the steps S5 and S6 for various eventssuch as occurrence of prostate cancer, occurrence of small cell subtype,and occurrence of Gleason scores greater than 7, multiple probabilitymaps for the various events are obtained or formed. The probabilitymaps, for example, include a prostate cancer probability map shown inFIG. 15A, a small cell subtype probability map shown in FIG. 15B, and aprobability map of Gleason scores greater than 7 shown in FIG. 15C. Someor all of the probability maps may be selected to be combined into acomposite probability image or map to provide most useful information tointerpreting Radiologist and Oncologist. The composite probability imageor map any show areas of interest. For example, the compositeprobability image or map shows areas with high probability of cancer(>98%), high probability of small cell subtype, and high probability ofGleason score >7, as shown in FIG. 15D.

In an alternative embodiment, the subset data DB-1 may further includemeasured values for a PET parameter (e.g., SUVmax) and a SPECTparameter. In this case, the classifier CF, e.g., Bayesian classifier,for the event (e.g., occurrence of prostate cancer) may be created basedon data associated with the event and specific variables, including,e.g., the PET parameter, the SPECT parameter, some or all of the MRIparameters depicted in the section of the “description of classifierCF”, and the processed parameters of average Ve and average Ktrans, inthe subset data DB-1. Next, by using the computing method depicted inFIG. 4, the probability map for the event may be generated or formedbased on values of the specific variables for each slop of the movingwindow 2.

In the invention, the computing method (i.e., the steps S1-S6) depictedin FIG. 4, for example, may be performed on a software, a device, or asystem including, e.g., hardware, one or more computing devices,computers, processors, software, and/or tools to obtain theabove-mentioned probability map(s) for the event(s) and/or theabove-mentioned composite probability image or map. Accordingly, adoctor questions the software, device or system about a suspected regionof an image such as MRI slice image, and the latter provides aprobability map for the event (e.g., occurrence of prostate cancer)and/or a likelihood measurement of cancer (e.g., malignancy) as ananswer.

In the case of the MRI image 10 obtained from the subject (e.g., humanpatient) that has been given a treatment, such as neoadjuvantchemotherapy or (preoperative) radiation therapy, or has taken or beeninjected with one or more drugs for a treatment, such as neoadjuvantchemotherapy, the effect of the treatment or the drugs on the subjectmay be evaluated, identified, or determined by analyzing the probabilitymap(s) for the event(s) depicted in the first embodiment and/or thecomposite probability image or map depicted in the first embodiment.Accordingly, a method of evaluating, identifying, or determining theeffect of the treatment or the drugs on the subject may include thefollowing steps: (a) administering to the subject the treatment or thedrugs, (b) after the step (a), obtaining the MRI image 10 from thesubject by the MRI system, (c) after the step (b), performing the stepsS2-S6 to obtain the probability map(s) for the event(s) depicted in thefirst embodiment and/or obtaining the composite probability image or mapdepleted in the first embodiment, and (d) after the step (c), analyzingthe probability map(s) for the event(s) and/or the composite probabilityimage or map.

The steps S1-S6 may be employed to generate a probability map of breastcancer. In this case, in the steps S1 and S2, the MRI image 10 shows thebreast anatomical structure of the subject its shown in FIG. 16, and thecomputation region 12, set in the desired or anticipated region 11,i.e., target region, of the MRI image 10, is defined with thecomputation pixels P_(k)

_(l) and covers at least 10, 25, 50, 80, 90 or 95 percent of the FOV ofthe MRI image 10, which includes the breast anatomical structure. Thesteps S3 and S4 are then sequentially performed. Next, in the step S5, aprobability of breast cancer for each stop of the moving window 2 may beobtained by matching the parameter set C_(m)

_(n) for said each stop W_(m)

_(n) of the moving window 2 from the step S4 (or the values C_(m)

_(n) of some or all of the specific MRI parameters for said each stopW_(m)

_(n) of the moving window 2 from the step S3) to the classifier CFcreated for breast cancer. In the step S6, the algorithm including thesteps S11-S16 illustrated in FIG. 8 is performed based on theprobabilities CL_(m)

_(n) of breast cancer for the stops W_(m)

_(n) of the moving window 2 to compute probabilities dl_(k)

_(l) of breast cancer for the respective computation pixels P_(k)

_(l), and the probabilities dl_(k)

_(l) of breast cancer for the respective computation pixels P_(k)

_(l) form the probability map of breast cancer.

FIG. 18 is a flow chart of evaluating, identifying, or determining theeffect of a treatment, such as neoadjuvant chemotherapy or(preoperative) radiation therapy, or a drug for the treatment on asubject (e.g., human or animal). Referring to FIG. 18, to a step S21, afirst MRI slice image is obtained from the subject by the MRI device orsystem. The first MRI slice image is composed of multiplemachine-defined original pixels p_(i)

_(j) in its field of view (FOV) to show an anatomical region of thesubject, such as prostate or breast. In a step S22, the steps S2-S6 areperformed on the first MRI slice image to generate a first probabilitymap.

After the step S21 or S22 is performed, step S23 is performed. In thestep S23, the subject is given the treatment, such as a drug givenintravenously or orally. For certain cancers such as prostate cancer,the treatment may be the (preoperative) radiation therapy (or calledradiotherapy), a proton beam therapy, a minimally invasive treatment(such as ablation in radiation), or an ablation therapy such ashigh-intensity focused ultrasound treatment. The (preoperative)radiation therapy for prostate cancer may be performed by a radiotherapydevice such as Truebeam or CyberKnife and may use high-energy radiation(e.g., gamma rays) to shrink tumors and kill cancer cells.

In a step S24, after the subject gets or receives the treatment such asan oral or intravenous drug, a second MRI slice image is obtained fromthe subject by the MRI device or system. The second MRI slice image iscomposed of multiple machine-defined original pixels p_(i)

_(j) in its FOV to show the same anatomical region of the subject as thefirst MRI slice image shows. In a step S25, the steps S2-S6 areperformed on the second MRI slice image to generate a second probabilitymap. The first and second probability maps may be generated for an eventor data type, such as prostate cancer, breast cancer, one of Gleasonscores 0 through 10, two or more of Gleason scores 0 through 10 (e.g.,Gleason scores greater than 7), tissue necrosis, or the percentage ofcancer in a specific range from a first percent (e.g., 91 percent) to asecond percent (e.g., 100 percent). Next, in a step S26, by comparingthe first and second probability maps, the effect of the treatment orthe drug used in the treatment on the subject may be identified,determined, or evaluated as effective or ineffective. Based on theresult from the step S26, a doctor can decide or judge whether thetreatment or the drug should be adjusted or changed. The method depictedin the steps S21-S26 can detect responses or progression after thetreatment or the drug within less than one week or two weeks, allowingearlier adjustments to the treatment regime.

FIG. 19 is a flow chart of evaluating, identifying, or determining theeffect of a treatment, such as neoadjuvant chemotherapy or(preoperative) radiation therapy, or a drug for the treatment on asubject (e.g., human or animal). Referring to FIG. 19, in a step S31, afirst MRI slice image is obtained from the subject by the MRI device orsystem. The first MRI slice image is composed of multiplemachine-defined original pixels p_(i)

_(j) in its field or view (FOV) to show an anatomical region of thesubject, such as prostate or breast. In a step S32, the steps S2-S5 areperformed on the first MRI slice image to obtain first probabilitiesCL_(m)

_(n) of an event or data type for stops W_(m)

_(n) of the moving window 2 for the computation region 12 of the firstMRI slice image. In other words, the first probabilities CL_(m)

_(n) of the event or data type for the stops W_(m)

_(n) of the moving window 2 on the first MRI slice image for the subjectbefore the treatment are obtained based on values C_(m)

_(n) of the specific MRI parameters for the stops W_(m)

_(n) of the moving window 2 on the first MRI slice image to match amatching dataset from the established classifier CF or biomarkerlibrary. The values C_(m)

_(n) of the specific MRI parameters for the stops W_(m)

_(n) of the moving window 2 on the first MRI slice image, for example,may be obtained from a registered (multi-parametric) image datasetincluding, e.g., the first MRI slice image and/or different parametermaps registered to the first MRI slice. The event or data type, forexample, may be prostate cancer, breast cancer, one of Gleason scores 0through 10, two or more of Gleason scores 0 through 10 (e.g., Gleasonscores greater than 7), tissue necrosis, or the percentage of cancer ina specific range from a first percent (e.g., 91 percent) to a secondpercent (e.g., 100 percent).

After the step S31 or S32 is performed, step S33 is performed. In thestep S33, the subject is given the treatment, such as a drug givenintravenously or orally. For certain cancers such as prostate cancer,the treatment may be the (preoperative) radiation therapy (or calledradiotherapy), a proton beam therapy, a minimally invasive treatment(such as ablation or radiation), or an ablation therapy such ashigh-intensity focused ultrasound treatment. The (preoperative)radiation therapy for prostate cancer may be performed by a radiotherapydevice such as Truebeam or CyberKnife and may use high-energy radiation(e.g., gamma rays) to shrink tumors and kill cancer cells.

In a step S34, after the subject gets or receives the treatment such asan oral or intravenous drug, a second MRI slice image is obtained fromthe subject by the MRI device or system. The second MRI slice image iscomposed of multiple machine-defined original pixels p_(i)

_(j) in its FOV to show the same anatomical region of the subject as thefirst MRI slice image shows. In a step S35, the steps S2-S5 areperformed on the second MRI slice image to obtain second probabilitiesCL_(m)

_(n) of the event or data type for stops W_(m)

_(n) of the moving window 2 for the computation region 12 of the secondMRI slice image. In other words, the second probabilities CL_(m)

_(n) of the event or data type for the stops W_(m)

_(n) of the moving window 2 on the second MRI slice image for thesubject after the treatment are obtained based on values C_(m)

_(n) of the specific MRI parameters for the stops W_(m)

_(n) of the moving window 2 on the second MRI slice image to match thematching dataset from the established classifier CF or biomarkerlibrary. The values C_(m)

_(n) of the specific MRI parameters for the stops W_(m)

_(n) of the moving window 2 on the second MRI slice image, for example,may be obtained from a registered (multi-parametric) image datasetincluding, i.e., the second MRI slice image and/or different parametermaps registered to the second MRI slice.

The stops W_(m)

_(n) of the moving window 2 for the computation region 12 of the firstMRI slice may substantially correspond to or may be substantiallyaligned with or registered to the stops W_(m)

_(n) of the moving window 2 for the computation region 12 of the secondMRI slice, respectively. Each of the stops W_(m)

_(n) of the moving window 2 for the computation region 12 of the firstMRI slice and the registered or aligned one of the stops W_(m)

_(n) of the moving window 2 for the computation region 12 of the secondMRI slice may substantially cover the same anatomical region of thesubject.

Next, in a step S36, the first and second probabilities CL_(m)

_(n) of the event or data type for each aligned or registered pair ofthe stops W_(m)

_(n) of the moving window 2 on the first and second MRI slice images aresubtracted from each other into a corresponding probability change PMCor CCL_(m)

_(n) for said each aligned or registered pair of the stops W_(m)

_(n) of the moving window 2 on the first and second MRI slice images.For example, for each aligned or registered pair of the stops W_(m)

_(n) of the moving window 2 on the first and second MRI slice images,the probability change PMC may be obtained by subtracting the firstprobability of the event or data type from the second probability of theevent or data type.

In a step S37, the algorithm, including the steps S11-S16, depicted inthe step S6 is performed based on the probability changes PMCs orCCL_(m)

_(n) for the aligned or registered pairs of the stops W_(m)

_(n) of the moving window 2 on the first and second MRI slice images tocompute probability changes PVCs or cdl_(k)

_(l) for respective computation pixels P_(k)

_(l) used to compose a probability change map for the event or datatype, as described below. Referring to FIG. 8, in the step S11, theprobability change PVC or cdl_(k)

_(l) for each of the computation pixels P_(k)

_(l) is assumed by, e.g., averaging the probability changes PMCs orCCL_(m)

_(n) of the aligned or registered pairs, of the stops of the movingwindows 2 on the first and second MRI slice images, each having theiraligned or registered squares 6 overlapping or covering said each of thecomputation pixels P_(k)

_(l). In the step S12, a probability change guess PG for each aligned orregistered pair of the stops W_(m)

_(n) of the moving window 2 on the first and second MRI slice images iscalculated by, e.g., averaging the probability changes PVCs or cdl_(k)

_(l) for all the computation pixels P_(k)

_(l) inside and each aligned or registered pair of the stops W_(m)

_(n) the moving window 2 on the first and second MRI slice images.

In the step S13, a difference DW between the probability change guess PGand the probability change PMC or CCL_(m)

_(n) for each aligned or registered pair of the stops W_(m)

_(n) of the moving window 2 on the first and second MRI slice images iscalculated by, e.g., subtracting the probability change PMC or CCL_(m)

_(n) for said each aligned or registered pair of the stops W_(m)

_(n) of the moving window 2 on the first and second MRI slice imagesfrom the probability change guess PG for said each aligned or registeredpair of the stops W_(m)

_(n) of the moving window 2 on the first and second MRI slice images. Inthe step S14, an absolute value of the difference DW for each aligned orregistered part of the stops W_(m)

_(n) of the moving window 2 on the first and second MRI slice images iscompared with the preset threshold error or value to determine whetheran error, i.e., the absolute value of the difference DW, between theprobability change guess PG and the probability change PMC or CCL_(m)

_(n) for each aligned or registered pair of the stops W_(m)

_(n) of the moving window 2 on the first and second MRI slice images isless than or equal to the preset threshold error or value. If theabsolute values of the differences DWs for all the aligned or registeredpairs of the stops W_(m)

_(n) of the moving window 2 on the first and second MRI slice images aredetermined in the step S14 to be less than or equal to the presetthreshold error or value, the step S16 continues. In the step S16, theprobability changes PVCs or cdl_(k)

_(l) for the computation pixels P_(k)

_(l) are determined to be optimal, which are called optimal probabilitychanges cdl_(k)

_(l) hereinafter, and the optimal probability changes cdl_(k)

_(l) of the computation pixels P_(k)

_(l) form the probability change map for the event or data type. Afterthe optimal probability changes cdl_(k)

_(l) for the computation pixels P_(k)

_(l) are obtained in the step S16, the algorithm is completed.

If any one of the absolute values of the differences DWs for all thealigned or registered pairs of the stops W_(m)

_(n) of the moving window 2 on the first and second MRI slice images isdetermined in the step S14 to be greater than the preset threshold erroror value, the step S15 continues. In the step S15, the probabilitychange PVC, i.e., updated cdl_(k)

_(l), for each of the computation pixels P_(k)

_(l) is updated or adjusted by, e.g., subtracting an error correctionfactor ECF for said each of the computation pixels P_(k)

_(l) from the current probability change PVC, i.e., current cdl_(k)

_(l), for said each of the computation pixels P_(k)

_(l). The error correction factor ECF for each of the computation pixelsP_(k)

_(l) is calculated by, e.g., summing error correction contributions fromthe aligned or registered pairs, of the stops W_(m)

_(n) of the moving window 2 on the first and second MRI slice images,each having their aligned or registered squares 6 covering oroverlapping said each of the computation pixels P_(k)

_(l), each of the error correction contributions to said each of thecomputation pixels P_(k)

_(l), for example, may be calculated by multiplying the difference DWfor a corresponding one of the aligned or registered pairs of the stopsW_(m)

_(n) of the moving window 2 on the first and second MRI slice images byan area ratio of an overlapped area between said each of the computationpixels P_(k)

_(l) and the corresponding one of the aligned or registered pairs of thestops W_(m)

_(n) of the moving window 2 on the first and second MRI slice images toa common area of the squares 4 inscribed in the corresponding one of thealigned or registered pairs of the stops W_(m)

_(n) of the moving window 2 on the first and second MRI slice images.After the probability changes PVCs or cdl_(k)

_(l) for the computation pixels P_(k)

_(l) are updated, the steps S12-S15 are performed repeatedly based onthe updated probability changes PVCs, i.e., updated cdl_(k)

_(l), for the computation pixels P_(k)

_(l) in the step S15, until the absolute values of the differences DWsfor all the aligned or registered pairs of the stops W_(m)

_(n) of the moving window 2 on the first and second MRI slice images aredetermined in the step S14 to be less than or equal to the presetthreshold error or value.

The above process uses the moving window 2 in the x and y directions tocreate a 2D probability change map. In addition, the above process maybe applied to multiple MRI slices of the subject registered in the zdirection, perpendicular to the x and y directions, to form a 3Dprobability change map.

In a step S38, by analyzing the probability change map, the effect ofthe treatment or the drug used in the treatment on the subject may beidentified, determined, or evaluated as effective or ineffective. Basedon the result from the step S38, a doctor can decide or judge whetherthe treatment or the drug should be adjusted or changed. The methoddepicted in the steps S31-S38 can detect responses or progression afterthe treatment or the drugs within less than one meek or two weeks,allowing earlier adjustments to the treatment regime.

FIG. 20 is a flow chart of evaluating, identifying, or determining theeffect of a treatment, such as neoadjuvant chemotherapy or(preoperative) radiation therapy, or a drug used in the treatment on asubject (e.g., human or animal). Referring to FIG. 20, in a step S41, afirst MRI slice image is obtained from the subject by the MRI device insystem. The first MRI slice image is composed multiple machine-definedoriginal pixels p_(i)

_(j) in its field of view (FOV) to show an anatomical region of thesubject, such as prostate or breast. In a step S42, the steps S2-S6 areperformed on the first MRI slice image to generate a first probabilitymap composed of first computation pixels P_(k)

_(l).

After the step S41 or S42 is performed, a step S43 is performed in thestep S43, the subject is given a treatment such as an oral orintravenous drug. For certain cancers such as prostate cancer, thetreatment may be the (preoperative) radiation therapy (or calledradiotherapy), a proton beam therapy, or an ablation therapy such ashigh-intensity focused ultrasound treatment. The (preoperative)radiation therapy for prostate cancer may be performed by a radiotherapydevice such as Truebeam or CyberKnife and may use high-energy radiation(e.g., gamma rays) to shrink tumors and kill cancer cells.

In a step S44, after the subject gets or receives the treatment such asan oral or intravenous drug, a second MRI slice image is obtained fromthe subject by the MRI device or system. The second MRI slice image iscomposed of multiple machine-defined original pixels p_(i)

_(j) in its FOV to show the same anatomical region of the subject as thefirst MRI slice image shows. In a step S45, the steps S2-S6 areperformed on the second MRI slice image to generate a second probabilityneap composed of second computation pixels P_(k)

_(l). Each of the second computation pixels P_(k)

_(l) may substantially correspond to or may be substantially alignedwith or registered to one of the first computation pixels P_(k)

_(l). The first and second probability maps may be generated for anevent or data type such as prostate cancer, breast cancer, one ofGleason scores 0 through 10, two or more of Gleason scores 0 through 10(e.g., Gleason scores greater than 7), tissue necrosis, or thepercentage of cancer in a specific range from a first percent (e.g., 91percent) to a second percent (e.g., 100 percent).

In a step S46, by subtracting a probability dl_(k)

_(l) for each of the first computation pixels P_(k)

_(l) from a probability dl_(k)

_(l) for the corresponding, registered or aligned one of the secondcomputation pixels P_(k)

_(l), a corresponding probability change cdl_(k)

_(l) is obtained or calculated. Accordingly, a probability change map isformed or generated based on the probability changes cdl_(k)

_(l). Next, in a step S47, by analyzing the probability change map, theeffect of the treatment or the drug used in the treatment on the subjectmay be identified, determined, or evaluated as effective or ineffective.Bused on the result from the step S47, is doctor can decide or judgewhether the treatment or the drug should be adjusted or changed. Themethod depicted in the steps S41-S47 can detect responses or progressionafter the treatment or the drug within less than one week or two weeks,allowing earlier adjustments to the treatment regime.

I-2. Probability Map Derived from Measured Values for Stops ofTwo-Dimensional Moving Window

Alternatively, FIG. 22B illustrates another process of using an Eoperator to obtain better resolution of probabilities of an event in atwo-dimensional region in accordance with an embodiment of the presentapplication. Referring to FIGS. 5, 6A and 22B, in a step S22-4, atwo-dimensional moving window 2 may be applied to a target region 11 ofa two-dimensional structure, such as biological structure or biopsytissue, by moving step by step on the target region 11 with a shiftequal to a x-direction width X_(fp), of the computation pixels P_(k)

_(l) of the two-dimensional computational map 12 and moving row by rowon the target region 11 with a shift equal to a y-direction width Y_(fp)of the computation pixels P_(k)

_(l) of the two-dimensional computational map 12 to measure one or a setof values C_(m)

_(n) of one or more imaging parameters, such as parameters of T1, T2 andKtrans for MRI parameters, parameters of T1, T2 and tau for MRIparameters or parameters obtained from one or more optical imagescaptured by one or more cameras, for each stop W_(m)

_(n) of the two-dimensional moving window 2. Each neighboring two of thestops W_(m)

_(n) in a x direction may partially overlap with each other with a shiftequal to a x-direction width X_(fp) of the computation pixels P_(k)

_(l) of the two-dimensional computational map 12. Each neighboring twoof the stops W_(m)

_(n) in a y direction may partially overlap with each other with a shiftequal to a y-direction width Y_(fp) of the computation pixels P_(k)

_(l) of the two-dimensional computational map 12.

One or more of computed tomography (CT) parameters, positron emissiontomography (PET) parameters, single-photon emission computed tomography(SPECT) parameters, micro-PET parameters, micro-SPECT parameters. Ramanparameters, and/or bioluminescence optical (BLO) parameters, ultrasoundparameters, camera-image parameters and/or visible-light-imageparameters may be measured for the one or the set of values C_(m)

_(n) for said each stop W_(m)

_(n) of the two-dimensional moving window. The one or the set of valuesC_(m)

_(n) of the one or more imaging parameters for said each stop W_(m)

_(n) of the two-dimensional moving window may be measured from detectionor analysis instruments, such as camera, microscope (optical orelectronic), endoscope, detectors or spectrometer (visible light,fluorescent light, IR, UV or X-ray), ultrasonic machine or system,magnetic resonance imaging (MRI) machine or system, computed tomography(CT) machine or system, positron emission tomography (PET) machine orsystem, single-photon emission computed tomography (SPECT) machine orsystem, micro-PET machine or system, micro-SPECT machine or system,Raman spectrometer or system, and/or bioluminescence optical (BLO)machine or system, or other machine for obtaining molecular orstructural imaging data.

Next, referring to FIG. 22B, the steps S22-2 and S22-3 as illustrated inFIG. 22A for the first aspect continue. Thereby, the algorithm may beemployed to transform the one or the set of values C_(m)

_(n) of the one or more imaging parameters for said each stop W_(m)

_(n) of the two-dimensional moving window into the probability dl_(k)

_(l) said each computation pixel P_(k)

_(l) of the two-dimensional computational map having better resolution.

Second Aspect: E Operator for Better Resolution of Measured Values inTwo-dimensional Region II-1. Computational Map Derived from MeasuredValues for Original Pixels of Two-Dimensional Original Map

Alternatively, the step S22-2 as illustrated in FIGS. 22A and 22B may beomitted. FIG. 23A illustrates a process of using an E operator to obtainbetter resolution of measured values in a two-dimensional region inaccordance with an embodiment of the present application. Referring toFIG. 23A, in a step S23-1 for convolution operation (E_(c)) atwo-dimensional moving window 2 is applied to a two-dimensional originalmap provided with multiple original measured values each for one of itsoriginal pixels p_(i)

_(j) arranged in a two-dimensional array, wherein the two-dimensionaloriginal map is registered to and associated with and covers a targetregion 11 for a biological structure, to obtain a value C_(m)

_(n) of an imaging parameter, such as parameter of T1, T2, Ktrans or taufor an MRI parameter or parameter obtained from an optical imagecaptured by a camera, for each stop W_(m)

_(n) of the two-dimensional moving window 2. In this case, the originalmeasured values for the respective original pixels p_(i)

_(j) of the two-dimensional original map may be associated with an MRIparameter; the two-dimensional original map may be associated with anMRI slice registered to or aligned with the target region 11. The valueC_(m)

_(n) of the imaging parameter for said each stop W_(m)

_(n) of the two-dimensional moving window 2 may be calculated orobtained based on one or more of the original measured values of theimaging parameter for respective one or more of the original pixelsp_(i)

_(j) of the two-dimensional original map, which are covered by orassociated with said each stop W_(m)

_(n) of the two-dimensional moving window 2. Said each stop W_(m)

_(n) of the two-dimensional moving window 2 has a larger area than thatof each of the respective one or more of the original pixels p_(i)

_(j) of the two-dimensional original map. Each neighboring two of thestops W_(m)

_(n) in a x direction may partially overlap with each other with a shiftequal to a x-direction width X_(fp) of computation pixels P_(k)

_(l) of a two-dimensional computational map 12. Each neighboring two ofthe stops W_(m)

_(n) in a y direction may partially overlap with each other with a shiftequal to a y-direction width Y_(fp) of the computation pixels P_(k)

_(l) of the two-dimensional computational map 12.

Next, referring to FIG. 23A, at a step S23-2 for deconvolution operation(E_(d) ), a value d_(k)

_(l) of the imaging parameter for each computation pixel P_(k)

_(l) of the two-dimensional computational map 12 is iteratively updatedor calculated, as illustrated in steps DC1-DC10 on following paragraphsin the second aspect, based on one or more of the values C_(m)

_(n) of the imaging parameter for respective one or more of the stopsW_(m)

_(n) each covering said each computation pixel P_(k)

_(l), wherein said each computation pixel P_(k)

_(l) has a smaller area than that of each of the respective one or moreof the stops W_(m)

_(n) of the two-dimensional moving window 2.

For more elaboration, the convolution matrix M_(cw) as illustrated inthe first aspect can be deconvoluted to obtain a limit or computationalmatrix M_(dp), The deconvolution matrix M_(dp) comprises a final orcomputational data, dataset or information for each final or computationpixel in the given 2D region. The data, dataset or information in orrelated to, or describing each pixel P_(k)

_(l) of the final or computation pixels in the given 2D region are ofthe same type, property, category or item (for example, MRI parameters)as that (for example, a MRI parameters) of the original data, dataset orinformation in the stops of moving window. The data, dataset orinformation in or related to, or describing each pixel P_(k)

_(l) of the final or computation pixels can be a number, multiplenumbers, a real number, multiple real numbers, a digitized number (forexample a negative integer, 0, or a positive integer), multipledigitized numbers, a 0 or 1, multiple 0’s or 1's, a scalar, multiplescalars, a vector, multiple vectors, or a tensor with degree of older 0,1, 2, . . . t, where t is an integer. The deconvolution E_(d) of the Eoperator obtains the data, dataset or information for each final orcomputation pixel by solving a set of linear equations with unknowncomputation pixel data (d_(k)

_(l)'s) and known convolution window data (C_(m)

_(n)'s). The linear equations can be established by equaling the data,dataset or information for each convolution window stop W_(m)

_(n) to the data, dataset or information averaged over all the final orcomputation pixels enclosed by the convolution window (W_(m)

_(n)), d_(k)

_(l). The averaging can be done by linear averaging, Gaussian averagingor Lorentian averaging of d_(k)

_(l)'s.

$\begin{matrix}{\mspace{79mu} {{{\frac{1}{P*Q}\text{?}\text{?}} = C_{mn}}{\text{?}\text{indicates text missing or illegible when filed}}}} & (5)\end{matrix}$

Wherein d_(k)

_(l)'s are the data, dataset or information of the final or computationpixels enclosed or within by the stop of the moving window W_(m)

_(n), wherein k is from k₁ to k₁+P−1, and l is from l₁ to l_(1+Q−)1, andm=1, 2, 3, . . . , K−P+1, and n=1 2, 3, . . . , L−Q+1.

There are (K−P+1)×(L−Q+1) equations with knows (C_(m)

_(n)'s), and K×L unknowns (d_(k)

_(l)'s). The number of unknowns is larger than the number or equations(5) by (PL+KQ−PQ−K−L+P+Q−1). A method to increase number of knows anddecrease number of unknowns will be described below by (1) findinguniform or constant data, dataset or information for the final orcomputation pixels in a region or regions of uniformity or approximatelyuniformity with the 2D region of interest, and/or (2) finding uniform orconstant data, dataset or information for the final or computationpixels in a region of regions of uniformity or approximately uniformityextending from and out of the boundary of the 2D region or interest. Theabove method (1) may provide a number of knows (known data for thecomputation pixels) equal to or larger than the number of(PL+KQ−PQ−K−L+P+Q−1) such that the number (K−P+1)×(L−Q+1) of theequations (5) may be solved. If the moving window comprises 3-by-3computation pixels, the above method (2) may provide a number of knows(known data for the computation pixels) equal to or larger than thenumber of [(K+1)(L+2)−(K−P+3)×(L−Q+3)] such that the number(K−P+3)×(L−Q+3) of the equations (5) may be solved. The set of linearequations can be solved by a computer, device, machine, processor,system or tool iteratively. The initial guess of each of the unknowns(the data, dataset or information of final or computation pixels), d

is obtained by averaging over all the stops of covering or enclosing thepixel. The contribution from each enclosing stop calculated by the arearatio of the overlapped area (A′_(m)

_(n)) to the area of that stop (A_(m)

_(n)). d

can be obtained using A_(m)

_(n), A′_(m)

_(n) and C_(m)

_(n).

$\begin{matrix}{{\text{?} = {\sum_{m_{1},n_{1}}^{m_{2},n_{2}}{\frac{\text{?}}{A_{m - n}}C_{m - n}}}}{\text{?}\text{indicates text missing or illegible when filed}}} & (1)\end{matrix}$

Wherein stops W_(m)

_(n) cover or enclose the final or computation pixel P_(k)

_(l) has stop indices m from m₁ to m₂, and n from n₁ to n₂. In the firstiteration, we can calculate and obtain the first data. dataset orinformation for each stop of the moving window, C_(m)

_(n)'s, by using initial guess d

's in equation (1). The iteration results in a solution M_(dp)(K×L) whenthe set of computation pixel data or information match the set ofconvolution window data or information with errors or difference smallerthan or equal to a specified value or number in the same 2D region. TheE_(d) operator can be expressed as

E _(d)(M _(cw) , W _(PQ))=M _(dp)

In another aspect of the disclosure, the convolution operator E_(c) andthe deconvolution operator E_(d) can be performed in sequence to get thefull E operator. The E operator transform the original matrix M_(op)(comprising elements of data, dataset or information for the I×Joriginal or initial pixels and has I×J sets elements or components ofdata or information) to the deconvolution matrix M_(dp) (comprisingelements of data, dataset or information for the K×L pixels and has K×Lsets or elements or components of data or information) in the same given2D region, through the convolution window matrix M_(cw) (comprising(K−P+1)×(L−Q+1) sets or elements or components of data or information inthe convolution window stops). The E operator can be expressed as

E(M _(op)(I×J))=E _(d)(M _(cw)((K−P+1)×(L−Q+1)))=E _(d) E _(c)(M_(op)(I×J))=M _(dp)(K×L)

In another aspect of the disclosure, this invention discloses the Eoperator in the linear algebra. The linear operations, such as addition(+), subtraction (−), multiplication by a scalar (d) or division by ascalar (/), are performed using the data or information of each stop ofthe moving window, (that is using the elements in the convolution matrixM_(cw)), instead of using the data or information of the original orinitial pixels (that is instead of using the elements in the convolutionmatrix M_(op)). The moving window is used as a default or standard size,shape, parameters, configuration or format for containing and providingdata, dataset or information an analysis, comparison, computing orengineering.

E(a Σ _(s) C _(s) M _(s))=M

Where M, or M is a matrix of the convolution M_(cw), and C_(s) are thereal numbers, s is an integer from 1, 2, 3, . . . , S, with S a positiveinteger.

The convolution operation (E_(c)) described and specified in the secondaspect is similar to the convolution operation (E_(c)) described in thefirst aspect using MRI detection and diagnosis as an example. Theconvolution operation (E_(c)) in the second aspect may be referred tothat as illustrated in the first aspect. The MRI parameters asillustrated in the first aspect may be employed for the values C_(m)

_(n) for the stops W_(m)

_(n) of the 2D moving window in the second aspect. A 2D moving windowmay be applied to a 2D object, e.g., 2D image 10, to obtain one ofvalues C_(m)

_(n) of a MRI parameter for example, for each of stops W_(m)

_(n) of the 2D moving window, as illustrated in the first aspect.

For more elaboration, with regard to the deconvolution operation (E_(d)) in the step S23-2 in FIG. 22, in a step DC1, one of the initial valuesd_(k)

_(l) for each of the computation pixels P_(k)

_(l) may be first calculated or assumed based on an average of thevalues C_(m)

_(n) for the stops W_(m)

_(n) of the moving window overlapping said each of the computationpixels P_(k)

_(l). Next, in a step DC2, a guess for each of the stops W_(m)

_(n) of the moving window may be calculated by averaging the initialvalues d_(k)

_(l) (obtained from the step DC1) for the computation pixels P_(k)

_(l) inside said each of the stops W_(m)

_(n) of the moving window. Next, in a step DC3, one of the guesses(obtained from the step DC2) for each of the stops W_(m)

_(n) of the moving window may be compared with one of the values C_(m)

_(n) for said each of the stops W_(m)

_(n) of the moving window by subtracting said one of the values C_(m)

_(n) for said each of the stops W_(m)

_(n) from said one of the guesses (obtained from the step DC2) for saideach of the stops W_(m)

_(n) to obtain a difference between said one of the values C_(m)

_(n) and said one of the guesses (obtained from the step DC2). Next, ina step DC4, a determination step may be performed to determine whetherthe absolute value of the difference (obtained from the step DC3) isless than or equal to a preset threshold error. If any of the absolutevalues of the differences (obtained from the step DC3) for therespective stops W_(m)

_(n) is greater than the preset threshold error, a step DC5 continues.If the absolute value of the difference (obtained from the step DC3) foreach of the stops W_(m)

_(n) is less than on equal to the preset threshold error a step DC10continues.

In the step DC5, an error correction factor (ECF) for each of thecomputation pixels P_(k)

_(l) is calculated by summing error correction contributions from thestops W_(m)

_(n) of the moving window overlapping said each of the computationpixels P_(k)

_(l). For a general example, if the moving window has a size of 2-by-2computation pixels, there may be neighboring four of the stops W_(m)

_(n) of the moving window overlapping one of the computation pixelsP_(k)

_(l). The error correction contribution from each of said neighboringfour of the stops W_(m)

_(n) to said one of the computation pixels P_(k)

_(l) may be calculated by multiplying the difference (obtained from thestep DC3) for said each of said neighboring four of the stops W_(m)

_(n) by a space ratio of an overlapped space between said one of thecomputation pixels P_(k)

_(l) and said each of said neighboring eight of the stops W_(m)

_(n) to a space of the moving window. Next, in a step DC6, one of theinitial values d_(k)

_(l) for each of the computation pixels P_(k)

_(l) may be updated by subtracting the error correction factor (ECF)(obtained from the step DC5) for said each of the computation pixelsP_(k)

_(l) from the initial value d_(k)

_(l) for said each of the computation pixels P_(k)

_(l). Next, in a step DC7, the guess for each of the stops W_(m)

_(n) of the moving window may be updated by averaging the updated valuesd_(k)

_(l) (obtained from the step DC6) for the computation pixels P_(k)

_(l) inside said each of the stops W_(m)

_(n) of the moving window. Next, in a step DC8, one of the updatedguesses (obtained from the step DC7) for each of the stops W_(m)

_(n) of the moving window may be compared with one of the values C_(m)

_(n) for said each of the stops W_(m)

_(n) of the moving window by subtracting said one of the values C_(m)

_(n) for said each of the stops W_(m)

_(n) from said one of the updated guesses (obtained from the step DC7)for said each of the stops W_(m)

_(n) to obtain an updated difference between said one of the valuesC_(m)

_(n) and said one of the updated guesses. Next, in a step DC9, adetermination step may be performed to determine whether the absolutevalue of the updated difference (obtained from the step DC8) is lessthan or equal to the preset threshold error. If any of the absolutevalues of the updated differences (obtained from the step DC8) for therespective stops W_(m)

_(n) is greater than the preset threshold error, the steps DC5-DC9continues for another iteration. If the absolute value of the updateddifference (obtained from the step DC8) for each of the stops W_(m)

_(n) is less than the preset threshold error, the step DC10 continues

In the step DC5 in the another iteration, the error correction factor(ECF) for each of the computation pixels P_(k)

_(l) may be updated by summing updated error correction contributionsfrom the stops W_(m)

_(n) of the moving window overlapping said each of the computationpixels P_(k)

_(l). For the above general example, the updated error correctioncontribution from said each of said neighboring eight of the stops W_(m)

_(n) to said one of the computation pixels P_(k)

_(l) may be calculated by multiplying the updated difference (obtainedfrom the step DC8 in the last iteration) for said each of saidneighboring eight of the stops W_(m)

_(n) by the space ratio. Next, in the step DC6 in the another iteration,one of the values d_(k)

_(l) for each of the computation pixels P_(k)

_(l) may be updated by subtracting the updated error correction factor(ECF) (obtained from the step DC5 in the current iteration) for saideach of the computation pixels P_(k)

_(l) from said one of the last updated values d_(k)

_(l) (obtained from the step DC6 in the last iteration) for said each ofthe computation pixels P_(k)

_(l). Next, in the step DC7 in the another iteration, the guess for eachof the stops W₁

₁

₁-W_(N)

_(N)

_(N) of the moving window may be updated by averaging the updated valuesd_(k)

_(l) (obtained from the step DC6 (in the current iteration) for thecomputation pixels P_(k)

_(l) inside said each of the stops W_(m)

_(n) of the moving window. Next, in the step DC8 in the anotheriteration, one of the updated guesses (obtained from the step DC7 in thecurrent iteration) for each of the stops W_(m)

_(n) of the moving window may be compared with one of the values C_(m)

_(n) for said each of the stops W_(m)

_(n) of the moving window by subtracting said one of the values C_(m)

_(n) for said each of the stops W_(m)

_(n) from said one of the updated guesses (obtained from the step DC7 inthe current iteration) for said each of the stops W_(m)

_(n) to obtain an updated difference between said one of the valuesC_(m)

_(n) and said one of the updated guesses (obtained from the step DC7 inthe current iteration). Next, in the step DC9 in the another iteration,a determination step may be performed to determine whether the absolutevalue of the updated difference (obtained from the DC8 in the currentiteration) is less than or equal to the preset threshold error. If anyof the absolute values of the updated differences (obtained from the DC8in the current iteration) for the respective stops W_(m)

_(n) is greater than the preset threshold error, the above steps DC5-DC9continues for iteration multiple times until the absolute value of theupdated difference (obtained from the DC8 in the current iteration) foreach of the stops W_(m)

_(n) is less than the preset threshold error. If the absolute value ofthe updated difference (obtained from the DC8 in the current iteration)for each of the stops W_(m)

_(n) is less than or equal to the preset threshold error, the step DC10continues.

In the step DC10, one of the updated values d_(k)

_(l) each of the computation pixels P_(k)

_(l) may be determined as an optimal value for said each of thecomputation pixels P_(k)

_(l), which may be constructed for a 2D computational map. In an examplefor an MRI parameter, each of the widths X_(fp) and Y_(fp) of thecomputation pixels P_(k)

_(l) in the x and y directions may range from 0.1 to 10 millimeters, andpreferably range from 0.5 to 3 millimeters. Alternatively, in an examplefor an infrared absorbance parameter, each of the widths X_(fp), andY_(fp) of the computation pixels P_(k)

_(l) in the x and y directions may range from 1 to 20 micrometers, andpreferably range from 1 to 5 micrometers

II-2. Computational Map Derived from Measured Values for Stops ofTwo-dimensional Moving Window

Alternatively, FIG. 23B illustrates another process of using an Eoperator to obtain better resolution of measured values in atwo-dimensional region in accordance with an embodiment of the presentapplication. Referring to FIGS. 5, 6A and 23B, in a step S23-3, atwo-dimensional moving window 2 may be applied to a target region 11 ofa two-dimensional structure, such as biological structure or biopsytissue, by moving step by step on the target region 11 with a shiftequal to a x-direction width X_(fp) of computation pixels P_(k)

_(l) of a two-dimensional computational map and moving row by row on thetarget region 11 with a shift equal to a y-direction width Y_(fp) of thecomputation pixels P_(k)

_(l) of the two-dimensional computational map to measure a value C_(m)

_(n) of an imaging parameter, such as parameter of T1, T2, Ktrans or taufor an MRI parameter or parameter obtained from an optical imagecaptured by a camera, for each stop W_(m)

_(n) of the two-dimensional moving window 2. Each neighboring two of thestops W_(m)

_(n) in a x direction may partially overlap with each other with a shiftequal to a x-direction width of the computation pixels P_(k)

_(l) of the two-dimensional computational map 12. Each neighboring twoof the stops W_(m)

_(n) in a y direction may partially overlap with each other with a shiftequal to a y-direction width Y_(fp) of the computation pixels P_(k)

_(l) of the two-dimensional computational map 12.

One or more of computed tomography (CT) parameters, positron emissiontomography (PET) parameters, single-photon emission computed tomography(SPECT) parameters, micro-PET parameters, micro-SPECT parameters, Ramanparameters, and/or bioluminescence optical (BLO) parameters, ultrasoundparameters, camera-image parameters and/or visible-light-imageparameters may be measured for the value C_(m)

_(n) for said each stop W_(m)

_(n) of the two-dimensional moving window. The value C_(m)

_(n) of the imaging parameter for said each stop W_(m)

_(n) of the two-dimensional moving window may be measured from detectionor analysis in such as camera, microscope (optical or electronic),endoscope, detectors or spectrometer (visible light, fluorescent light,IR, UV or X-ray), ultrasonic machine or system, magnetic resonanceimaging (MRI) machine or system, computed tomography (CT) machine orsystem, positron emission tomography (PET) machine or system,single-photon emission computed tomography (SPECT) machine or system,micro-PET machine or system, micro-SPECT machine or system, Ramanspectrometer or system, and/or bioluminescence optical (BLO) machine orsystem, or other machine for obtaining molecular or structural imagingdata.

In an example, a biopsy tissue may be fixed on a glass slide and the 2Dimage for the biopsy tissue may be captured by a camera or microscope.An infrared (IR) detector may generate a two-dimensional moving windowto be applied to a two-dimensional target region, e.g., biopsy tissue,to measure a value C_(m)

_(n) of an IR absorbance parameter at a specific spectrum, for example,for each stop W_(m)

_(n) of the two-dimensional moving window.

Next, the step S23-2 as illustrated in FIG. 23A for the second aspectcontinues. Thereby, the algorithm in the second aspect may be employedto transform the value C_(m)

_(n) the imaging parameter for the stops W_(m)

_(n) of the 2D moving window into the value d_(k-1) of the imagingparameter for the computation pixel P_(k)

_(l). The value d_(k)

_(l) of the imaging parameter may be calculated as mentioned above inthe second aspect/

Third Aspect: E Operator for Better Resolution of Measured Values inThree-Dimensional Space III-1. Computational Map Derived from MeasuredValues for Original Voxels of Three-Dimensional Original Map

FIG. 24 illustrates a schematic view showing a three-dimensional (3D)image of a three-dimensional object in accordance with the presentapplication. FIG. 25 illustrates a schematic view showing athree-dimensional (3D) moving window in accordance with an embodiment ofthe present application. FIGS. 26A-26C are schematic views showing aprocess of applying a three-dimensional moving window to athree-dimensional image to obtain better resolution in the 3D image inaccordance with an embodiment of the present application. Referring toFIGS. 23A, 24, 25 and 26A-26C, in the step S23-1 for convolutionoperation (E_(c)), a three-dimensional moving window 102 is applied to athree-dimensional original map provided with multiple original measuredvalues of an imaging parameter, such as parameter of T1, T2, Ktransand/or tau for an MRI parameter or parameter obtained from a wavepenetrating device configured to generate a wave to penetrate a targetspace 100, each for one of its original voxels p_(i)

_(j)

_(g) arranged in a three-dimensional array, wherein thethree-dimensional original map is registered to and associated with andcovers the target space 100 fur a biological structure, to obtain avalue C_(m)

_(n)

_(u) of the imaging parameter for each stop W_(m)

_(n)

_(u) of the three-dimensional moving window 102. In this case, theoriginal measured values for the respective original voxels p_(i)

_(j)

_(g) of the three-dimensional original map may be associated with an MRIparameter; the three-dimensional original map may be associated with acombination of multiple MRI slices registered to or aligned with thetarget space 100. The value C_(m)

_(n)

_(u) of the imaging parameter for said each stop W_(m)

_(n)

_(u) of the three-dimensional moving window 102 may be calculated orobtained based on one or more of the original measured values of theimaging parameter for respective one or more of the original voxelsp_(i)

_(j)

_(g) of the three-dimensional original map, which are covered by orassociated with said each stop of the three-dimensional moving window102. Said each stop W_(m)

_(n)

_(u) of the three-dimensional moving window 102 has a larger volume thanthat of each of the respective one or more of the original voxels p_(i)

_(j)

_(g) of the three-dimensional original map. Each neighboring two of thestops W_(m)

_(n)

_(u) in a x direction may partially overlap with each other with a shiftequal to a x-direction width X_(fp) of computation voxels P_(k)

_(l)

_(h) of a three-dimensional computational map. Each neighboring two ofthe stops W_(m)

_(n)

_(u) in a y direction may partially overlap with each other with a shiftequal to y-direction width Y_(fp) of the computation voxels P_(k)

_(l)

_(h) of the three-dimensional computational map. Each neighboring two ofthe stops W_(m)

_(n)

_(u) in a z direction may partially overlap with each other with a shiftequal to a z-direction width Z_(fp) of the computation voxels P_(k)

_(l)

_(h) the three-dimensional computational map.

Next, referring to FIG. 23A, in the step S23-2 for deconvolutionoperation (E_(d)), a value d_(k)

_(l)

_(h) of the imaging parameter for each computation voxel P_(k)

_(l)

_(h) of the three-dimensional computational map it iteratively updatedor calculated, as illustrated in steps DC1-DC10 in the third aspect,based on one or more of the values C_(m)

_(n)

_(u) of the imaging parameter for respective one or more of the stopsW_(m)

_(n)

_(u) each covering said each computation voxel P_(k)

_(l)

_(h), wherein said each computation voxel P_(k)

_(l)

_(h) has a smaller volume than that of each of the respective one ormore of the stops W_(m)

_(n)

_(u) of the three-dimensional moving window 102.

Another aspect of the disclosure provides an algorithm, a method, or anoperator, for transformation of data, dataset or information related tooriginal or initial voxels (p_(i-j-g)) at respective locations,x_(i-j-g) of a 3D space to a data, dataset or information in a final orcomputation voxels (P_(k)

_(l)

_(h)) at related locations X_(k)

_(l)

_(h)'s, of the same 3D space, wherein i, j, g, k, l, h are positiveintegers, i from 1, 2, . . . , to 1, j from 1, 2, . . . , to J: g from1, 2, . . . , to G: k from 1, 2, . . . , to K: l from 1, 2, . . . , toL: and h from 1, 2, . . . , to H. The transformation results in a newset of data, dataset or information of the final or computation voxelswith a better resolution and a lower noise as compared to that of theoriginal or initial vowels. K may be different from L L may be differentfrom J and H may be different from G. For a better resolution and alower noise, the volume of each of the final or computation voxels issmaller than that of the original or initial voxels; that is K>I, I>jand H>G. Alternatively, when I=K, J=L and H=G, X_(k)

_(l)

_(h) can be the same as x_(i-j)

, wherein the noises due to measurement fluctuation in the data, datasetor information of the original or initial voxels are smeared-out. The 3Dspace may comprise I×J×G voxels in grids of original or initial voxels,wherein the size and numbers of voxels may be determined by a certaindetector or sensor used in obtaining the data, dataset or informationrelated to the original or initial voxels, wherein the original orinitial voxels are the same as the measuring voxels in detection using acertain detector or sensor. Alternatively, the size and numbers ofvoxels may be chosen for forming a 3D space or matrix, wherein the data,dataset or information of the original or initial voxels may be obtainedbased on the data, dataset or information of the measuring voxels indetection using a certain detector or sensor. For example, the data,dataset or information of the original or initial voxel may becalculated by volume averaging of the data, dataset or information ofmeasuring voxels overlapping the original or initial voxel, full orpartial. The 3D space may as well comprise K×L×H voxels in grids offinal or computation voxels, wherein the size and numbers of voxels maybe generated for a desired resolution for analysis, diagnosis or aspecific application. The data, dataset or information related to theoriginal or initial voxels may be of a certain type, property, categoryor item (for example, MRI parameters) obtained from a certain detectoror sensor. The data, dataset or information related to the final orcomputation voxels may be of a same type, property, category or item (asthat, for example the MRI parameters, of the original in initial vowels)obtained from the transformation or computation. Alternatively, thedata, dataset or information related to the original or initial voxelsmay be, for examples, the IR absorption images for a given range ofwavenumbers, the Raman scattering images for a given range ofwavenumbers, the fluorescent light images for a given range ofwavenumbers, or the ultrasonic images of a human organ. The original orinitial voxels have a dimension one direction (for example, x direction)x_(op), dimension in a direction perpendicular to x-direction (forexample, y direction) y_(op) and a dimension in a directionperpendicular to the xy plane (for example, z direction) z_(op); whilethe final voxels have a dimension in one direction (for example, xdirection) X_(fp), a dimension in a direction perpendicular tox-direction (for example, y direction) Y_(fp), and a dimension in adirection perpendicular to the xy plane (for example, z direction)Z_(fp). The final voxels may have the same dimensions (size) as that ofthe original voxels, or with each voxel having a size larger or smallerthan the size of original or initial voxels, while both are in the same3D space. The data, dataset or information in or related to, ordescribing each of the original or initial voxels (p_(i-j-g)) can be anumber, multiple numbers, a real number, multiple real numbers, adigitized number (for example a negative integer, 0, or a positiveinteger), multiple digitized numbers, a 0 or 1, multiple 0's or 1's, ascalar, multiple scalars, a vector, multiple vectors, or a tensor withdegree of order 0, 1, 2, . . . , t, where t is an integer.

The disclosed algorithm or operator comprises two operations, aconvolution operation (E_(c)) and deconvolution operation (E_(d)). E_(c)and E_(d) can be operated separately or together. When combining thesetwo operations together, it is the Engineering operator (E operator),E=E_(d) E_(c). The E operator, as well as the E_(c) and E_(d) operatorswill be described and specifies as follows.

The original data, dataset or information in the original or initialyowls in a given 3D space is transformed to a data, dataset orinformation in stops of a 3D moving window, with the data, dataset orinformation of the same type, property, category or item (for example,MRI parameters) as that (fun example, a MRI parameters) of the originaldata, dataset or information in the original or initial voxels. The 3Dmoving window plays a key role in the E operator or E algorithm. It isdefined with some physical, computation, analytical, or statisticalpurposes for better resolution and lower noise. The size, volume, shape,parameters or format of the 3D moving window may become a default orstandard size, volume, shape, parameters or format in collecting,storing, computing, (statistically) analyzing data or information, orengineering learning or machine learning. Usually, the size, volume,shape, parameters or format of the 3D moving window is chosen to encloseat least several original or initial voxels, as well as at least severalfinal or computation voxels. For example, the 3D moving window size,volume and shape can be defined with a volume (x-dimension of the 3Dmoving window times y-dimension of the 3D moving window timesz-dimension of the 3D moving window) equal to a volume of a biopsysample; wherein the volume of the biopsy sample may be defined by theaveraged volume of biopsy samples taken in the standard biopsy procedureusing needles having popular or standard sizes. The 3D moving windowvolume mentioned above is defined as the size, volume, shape, parametersor format of the 3D moving window in the 3D space. The 3D moving windowmay have a shape of a sphere, an ellipsoid, a cube or a cuboid. When the3D moving widow has a shape of sphere, the maximum inscribed cube maycontain p×p×p original or initial voxels, or P×P×P final or computationvoxels; wherein p and P are positive numbers, and is greater than orequal to 1. P, in some cases, is chosen to be a positive integer, and isgreater than or equal to 2. When the 3D moving widow has a shape ofellipsoid, the maximum inscribed cuboid may contain p×q×r original orinitial voxels; or P×Q×R final or computation voxels where p, q, r, P, Qand R are positive numbers, and are greater than or equal to 1. P, Q andR, in some cases, are chosen to be positive integers, and are greaterthan or equal to 2. When the 3D moving widow has a shape of the cube,the cube may contain p×p×p original or initial vowels; or P×P×P final orcomputation voxels; where p, and P are positive numbers, and are greaterthan or equal to 1. P, in some cases, is chosen to be a positiveinteger, and is greater than or equal to 2. When the 3D moving widow hasa shape of cuboid, the cuboid may contain p×q×r original or initialvoxels; or P×Q×R final or computation voxels; where p, q, r, P, Q and Rare positive numbers, and greater than or equal to 1. P, Q and R, insome cases, are chosen to be positive integers, and are greater than orequal to 2. The 3D moving widow are stepping in the same 3D space by astep of X_(fp) in the x direction, a step of Y_(fp) in the y direction,and a step of Z_(fp) in the z direction, and resulting in an array ofdensely populated and overlapped (3D) stops. Each stop overlaps itsnearest neighbor stop with a step or shift of X_(fp), Y_(fp) or Z_(fp)in the x, y and z directions, respectively. Each stop in the 3D spacecomprises a number of original voxels, full or partial. The data,dataset or information for each stop is obtained by averaging over allthe voxels enclosed by the stop. For some partially enclosed voxels, theaveraging computation over these voxels can be done by weighing theenclosed volume proportionally. The averaging can be done by linearaveraging, Gaussian averaging or Lorentian averaging. In linearaveraging, we assume the data, dataset or information in each stop of 3Dmoving window is uniform. The above method transforms data, dataset orinformation in the original or initial voxels to data, dataset orinformation in stops of 3D moving window; wherein the transform can becalled a convolution. The stop of 3D moving window at location X_(m)

_(n)

_(u) is defined as W_(m)

_(n)

_(u), wherein m=1, 2, 3, 4, . . . , M, n=1, 2, 3, 4, . . . , N, and u=1,2, 3, 4, . . . , U. The data, dataset or information in or related toeach stop (W_(m)

_(n)

_(u)) of the 3D moving window can be a number, multiple numbers, a realnumber, multiple real numbers, a digitized number (for example anegative integer, 0, or a positive integer), multiple digitized numbers,a 0 or 1, multiple 0's or 1's, a scalar, multiple scalars, a vector,multiple vectors, or a tensor with degree of order 0, 1, 2, . . . , t,where t is an integer. Since the ID moving window is stepping by thesize of a final or computation voxel, the number of the stops is countedin a 3D array of final or computation voxels. Each stop of movingcomprises P×Q×R final or computation voxels. The original matrix M_(op)comprises I×J×G voxels and has I×J×G sets or elements or components ofdata, dataset or information. The convolution matrix M_(cw) comprises(K−P+1)×(L−Q+1)×(H−R+1) stops of moving window, and has(K−P+1)x(L−Q+1)×(H−R+1) sets of elements or components of data, datasetor information. The E_(c) operator transforms original matrix M_(op)(comprising I×J×G sets or elements of data, dataset or information (forexample, MRI parameters) describing or representing each original voxelin the given 3D space) to a convolution matrix M_(cw) (comprising(K−P+1)×(L−Q+1)×(H−R+1) sets or elements of averaged data, dataset orinformation (for example, MRI parameters) describing or representingeach stop of 3D moving window in the given 3D space) can be expressedas:

E _(c)(M _(op) , E _(PQR))=M _(cw)

Wherein M_(op) has dimension or I×J×G, the 3D moving window W_(PQR) hasdimension or size P×Q×R, and M_(cw) has dimension or size((K−P+1)×(L−Q+1)×(H−R+1). The comprises elements of data, dataset, orinformation of the same type, property, category or item as that ofM_(op). For example, the elements in both M_(cw) and M_(op) are data,dataset or information related to the MRI parameters. Alternatively, theelements in both M_(cw) and M_(op) are data, dataset or informationrelated to the IR absorption, Raman scattering, fluorescent light, orultrasonic imaging.

In another aspect of the disclosure, the convolution matrix M_(cw) canbe deconvoltioned to obtain a final or computational matrix M_(dp). Thedeconvolution matrix M_(dp) comprises a final or computational data,dataset or information for each final or computation voxel in the given3D space. The data, dataset or information in or related to, ordescribing each voxel P_(k)

_(l)

_(h) of the final or computation voxels in the given 3D space are of thesame type, property, category or item (for example, MRI parameters) asthat (for example, a MRI parameters) of the original data, dataset orinformation in the stops of 3D moving window. The data, dataset orinformation in or related to, or describing each voxel P_(k)

_(l)

_(h) of the final or computation voxels can be a number, multiplenumbers, a real number, multiple real numbers, a digitized number (forexample a negative integer, 0, or a positive integer), multipledigitized numbers, a 0 or 1, multiple 0's or 1's, a scalar, multiplescalars, a vector, multiple vectors, or a tensor with degree of order 0,1, 2, . . . , t, where t is an integer. The deconvolution E_(d) of the Eoperator obtains the data, dataset or information for each final orcomputation voxel by solving a set of linear equations with unknowncomputation pixel data (d_(k)

_(l)

_(h)'s) and known convolution window data (C_(m)

_(n)

_(u)'s). The linear equations can be established by equaling the data,dataset or information for each convolution window stop W_(m)

_(n)

_(u) to the data, dataset or information averaged over all the final orcomputation voxels enclosed by the convolution window (W_(m)

_(n)

_(u)), d_(k)

_(l)

_(h). The averaging can be done by linear averaging, Gaussian averagingor Lorentian averaging of d_(k)

_(l)

_(h)'s.

$\mspace{20mu} {{\frac{1}{P*Q*R}\text{?}\text{?}} = C_{m - n - u}}$?indicates text missing or illegible when filed

Wherein d_(k)

_(l)

_(h)s are the data, dataset or information of the final or computationvoxels enclosed or within by the stop W_(m)

_(n)

_(u) of the 3D moving window, wherein k is from k₁ to k₁+P−1, l is froml₁+Q−1, h is from h₁ to h₁+R−1, and m=1, 2, 3, . . . , K−P+1; n=1, 2, 3,. . . , L−Q+1, and u=1, 2, 3, . . . , H−R+1.

There are (K−P+1)×(L−Q+1)×(H−R+1) equations with knows (C_(m)

_(n)

_(u)'s), and K×L×H unknowns (d_(k)

_(l)

_(h)'s). The number of unknowns is larger than the number of equations.A method to increase number of knows and decrease number of unknownswill be described below by (1) finding uniform or constant data, datasetor information for the final or computation voxels in a region orregions of uniformity or approximately uniformity with the 3D space ofinterest, and/or (2) finding uniform or constant data, dataset orinformation for the final or computation voxels in a region or regionsof uniformity or approximately uniformity extending from and out of theboundary of the 3D space of interest. The set of linear equations can besolved by a computer, device, machine, processor, system or tooliteratively. The initial guess of each of the unknowns (the data,dataset or information of final or computation pixels), d_(k)

_(l)

, is obtained by averaging over all the stops of covering or enclosingthe voxel. The contribution from each enclosing stop calculated by thevolume ratio of the overlapped volume (V′_(m)

_(n)

_(u)) to the volume of that stop (V_(m)

_(n)

_(u)). d_(k)

_(l)

can be obtained using V_(m)

_(n)

_(u), V′_(m)

_(n)

_(u) and C_(m)

_(n)

_(u).

$\begin{matrix}{\mspace{79mu} {{\text{?} = {\sum_{m_{1},n_{1},u_{1}}^{m_{2},n_{2},u_{2}}{\frac{\text{?}}{v_{m - n - u}}C_{m - n - u}}}}{\text{?}\text{indicates text missing or illegible when filed}}}} & (3)\end{matrix}$

Wherein stops W_(m)

_(n)

_(u)'s covering or enclosing the final or computation voxel P_(k)

_(l)

_(h) has stop indices m from m₁ to m₂, n from n₁ to n₂ and u from u₁ tou₂. For examples, if the moving window comprises 8 computation voxels(2×2×2), a given computation voxel will be overlapped by 8 (2³) windowstops; if the moving window comprises 27 computation voxels (3×3×3), agiven computation voxel will be overlapped by 27 (3³) window stops, ifthe moving window comprises 24 computation voxels (2×3×4), a givencomputation voxel will be overlapped by 24 (2×3×4) window stops. In thefirst iteration we can calculate and obtain the first data, dataset eachstop of the 3D moving window, C_(m)

_(n)

_(u)'s, by using initial guess x_(k)

_(l)

's in equation (3). The iteration results in a solution M_(dp)(K×L×H)when the set of computation voxel data or information match the set ofconvolution window data or information with errors or difference smallerthan or equal to a specified value or number in the same 3D space. TheE_(d operator can be expressed as:)

E _(d)(M _(cw) , W _(PQR))=M _(dp)

In another aspect of the disclosure, the convolution operator E_(c) andthe deconvolution operator E_(d) can be performed in sequence to get thefull E operator. The E operator transform the original matrix M_(op)(comprising elements of data, dataset or information for the I×J×Goriginal or initial voxels and has I×J×G sets or elements or componentsof data or information) to the deconvolution matrix M_(dp) (comprisingelements or data, dataset or information for the K×L×H voxels and hasK×L×H sets or elements or components of data or information) in the samegiven 3D space, through the convolution window matrix M_(cw) (comprising(K−P+1)×(L−Q+1)×(H−R+1) sets or elements or components of data orinformation in the convolution window stops). The E operator can beexpressed as

E(M _(op)(I×J×K))=E _(d)(M _(cw)((K−P+1)×(L−Q+1)×(H−R+1)))=E _(d) E_(c)(M _(op)(I×J×K))=M _(dp)(K×L×H)

In another aspect of the disclosure, this invention discloses the Eoperator in the linear algebra. The linear operations, such as addition(+), subtraction (−), multiplication by a scalar (d) or division by ascalar (/), are performed using the data or information each stop of the3D moving window, (that is using the elements in the convolution matrixM_(cw)), instead of using the data or information of the original orinitial voxels (that is instead of using the dements in the convolutionmatrix M_(op)). The 3D moving window is used as a default or standardsize, volume, shape, parameters, configuration or format for containingand providing data, dataset or information for analysis, comparison,computing or engineering.

E(a Σ _(s) C _(s) M _(s))=M

Where M, or M is a matrix of the convolution M_(cw), and C_(s) are thereal numbers, s is an integer from 1, 2, 3, . . . , S, with S a positiveinteger.

Referring to FIG. 24, the three-dimensional object may be an organ, suchas brain, liver, lung, kidney, breast or prostate, of a human or animal.The 3D image 100 may be created by an MRI machine stepping in a zdirection for forming multiple MRI slices 10 arranged in the zdirection.

The MRI parameters as illustrated in the First aspect may be employedfor the values C_(m)

_(n)

_(u) for the stops W_(m)

_(n)

_(u) of the 3D moving window in the third aspect.

Alternatively, one or more of computed tomography (CT) parameters,positron emission tomography (PET) parameters, single-photon emissioncomputed tomography (SPECT) parameters, micro-PET parameters,micro-SPECT parameters, Raman parameters, and/or bioluminescence optical(BLO) parameters, ultrasound parameters, inflated absorbance parameters,camera-image parameters and/or visible-light-image parameters may alsobe measured for the value C_(m)

_(n)

_(u) for said each stop W_(m)

_(n)

_(u) of the three-dimensional moving window in the third aspect. Thedata, dataset or information C_(m)

_(n)

_(u) for the stops W_(m)

_(n)

_(u) of the three-dimensional moving window in the third aspect may beobtained from detection or analysis instruments, such as camera,microscope (optical or electronic), endoscope, detectors or spectrometer(visible light, fluorescent light, IR, UV or X-ray), ultrasonic machineor system, magnetic resonance imaging (MRI) machine or system, computedtomography (CT) machine or system, positron emission tomography (PET)machine or system, single-photon emission computed tomography (SPECT)machine or system, micro-PET machine or system, micro-SPECT machine orsystem, Raman spectrometer or system, and/or bioluminescence optical(BLO) machine or system, or other machine for obtaining molecular orstructural imaging data.

The algorithm in the third aspect may be employed to transform the data,dataset or information C_(m)

_(n)

_(u) for the stops W_(m)

_(n)

_(u) of the 3D moving window into the data, dataset or information d_(k)

_(l)

_(h) for the computation voxel P_(k)

_(l)

_(h). The data, dataset or information d_(k)

_(l)

_(h) may be calculated as mentioned above in the third aspect.

For more elaboration, an example is mentioned as below:

Referring to FIG. 25, the moving window MV may be a three-dimensional(3D) moving window 102 having a cubic shape with 2-by-2-by-2 cubes. Thethree-dimensional (3D) moving window 102 may be divided into multiplesmall units or cubes 106. The number of the small cubes 106 in the 3Dmoving window 102 may be equal to n

, where n is equal to an integer, such as 2, 3, 4, 5, 6, or more than 6.Each of the small cubes 106 may have a width X_(fp) in a x direction, awidth Y_(fp) in a y direction and a width Z_(fp) in the z direction. Thewidth X_(fp) may be substantially equal to the width Y_(fp)substantially equal to Z_(fp). Based on the size (e.g., the widthsX_(fp), Y_(fp) and Z_(fp)) and shape of the cubes 6, the size and shapeof computation voxels P_(k)

_(l)

_(h) for composing a 3D computational map may be defined. In otherwords, each of the computation voxels P_(k)

_(l)

_(h) for composing the computational map, for example, may be defined asa cube with the width X_(fp) in the x direction, the width Y_(fp) in they direction and the width Z_(fp) in the z direction and with a volumesubstantially the same as that of each cube 106.

Referring to FIG. 25, each of the cubes 106 may have a volume of 1millimeter by 1 millimeter by 1 millimeter, that is, each of the cubes106 may have the widths X_(fp), Y_(fp) and Z_(fp) of 1 millimeter. Eachof the widths X_(fp), Y_(fp), and Z_(fp) may range from 1 micrometer to10 millimeter, and the widths X_(fp), Y_(fp), and Z_(fp) may be thesame. Alternatively, any two of the widths X_(fp), Y_(fp), and Z_(fp)may be the same, but the other one of the widths X_(fp), Y_(fp) andZ_(fp) may be different from said any two of the widths X_(fp), Y_(fp),and Z_(fp). Alternatively, each two of the widths X_(fp), Y_(fp), andZ_(fp) may be different from each other. In an example for an MRIparameter, each of the widths X_(fp), Y_(fp) and Z_(fp) of thecomputation voxels P_(k)

_(l)

_(h) in the x, y and z directions may range from 0.1 to 10 millimeter,and preferably range from 0.5 to 3 millimeters.

Referring to FIGS. 22A, 24, 25 and 26A-26C, in the step S23-1 forconvolution operation (E_(c)), the three-dimensional moving window 102may be applied to the three-dimensional object shown in the 3D image 100as seen in FIG. 24 to obtain one of values C_(m)

_(n)

_(u) for each of stops W_(m)

_(n)

_(u) of the 3D moving window 102, wherein each neighboring two of thestops W_(m)

_(n)

_(u) in the x, y or z direction may partially overlap with each other.The 3D moving window 102 may perform the following steps:

(1) moving step by step with a distance equal to the width X_(fp) of thecube 106 in the x direction (equal to the width of the computationvoxels P_(k)

_(l)

_(h) in the x direction) from a left side of the 3D image 100 to a rightside of the 3D image 100 in a row to obtain one of the values C_(m)

_(n)

_(u) for each of the stops W_(m)

_(n)

_(u) of the 3D moving window 102 in the row, for an example, the 3Dmoving window 102 may move step by step, in a frontmost two of the MRIslices 10 aligned in the z direction for the 3D image 100, with adistance equal to the width X_(fp) of the cube 106 in the x direction(equal to the width of the computation vowels P_(k)

_(l)

_(h) in the x direction) from the left side of the 3D image 100 to theright side of the 3D image 100 in the topmost row to obtain one of thevalues C₁₋₁₋₁-C_(N-1-1) for each of the stops W₁₋₁₋₁-W_(N-1-1) of the 3Dmoving window 102 as seen in FIG. 26A;

(2) moving to the next row of the 3D image 100 with a distance equal tothe width Y_(fp) of the cube 106 in the y direction (equal to the widthof the computation voxels P_(k)

_(l)

_(h) in the y direction) to repeat the step (1) to obtain one of thevalues C_(m)

_(n)

_(u) for each of the stops W_(m)

_(n)

_(u) of the 3D moving window 102 in the next bottom row, wherein thesteps (1) and (2) repeat as seen in FIG. 26A until the 3D moving window102 moves to the bottommost row of the 3D image 100 to repeat the step(1) to obtain one of the values C_(m)

_(n)

_(u) for each of the stops W_(m)

_(n)

_(u) of the 3D moving window 102 in a plane; for the example, the 3Dmoving window 102 may move to the second topmost row with a distanceequal to the width Y_(fp) of the cube 106 in the y direction (equal tothe width of the computation voxels P_(k)

_(l)

_(h) the y direction) in the frontmost two of the MRI slices 10 alignedin the z direction for the 3D image 100 to repeat the step (1) to obtainone of the values C₁₋₂₋₁-C_(N-2-1) for each of the stopsW₁₋₂₋₁-W_(N-2-1) of the 3D moving window 102; the 3D moving window 102may repeat the step (1) row by row in the frontmost two of the MRIslices 10 aligned in the z direction for the 3D image 100 until the 3Dmoving window 102 moves to the bottommost row of the 3D image 100 toobtain one of the values C₁₋₁₋₁-C_(N-N-1) for each of the stopsW₁₋₁₋₁-W_(N-N-1) of the 3D moving window 102 as seen in FIG. 26A.

(3) moving to the next combination of the MRI slices 10 aligned in thedirection for the 3D image 100 with a distance equal to the widthZ_(fp), of the cube 106 in the z direction (equal to the width of thecomputation voxels P_(k)

_(l)

_(h) in the z direction) to repeat the steps (1) and (2) to obtain oneof the values C_(m)

_(n)

_(u) for each of the stops W_(m)

_(n)

_(u) of the 3D moving window 102, wherein the steps (1), (2) and (3)repeat until the 3D moving window 102 move to the backmost combinationof the MRI slices 10 aligned in the z direction for the 3D image 100 torepeat the steps (1) and (2) in the backmost combination of the MRIslices 10 aligned in the z direction for the 3D image 100; for theexample, the 3D moving window 102 may repeat the steps (1) and (2) planeby plane with a distance equal to the width Z_(fp) of the cube 106 inthe z direction (equal to the width of the computation voxels P_(k)

_(l)

_(h) in the z direction) from the frontmost two of the MRI slices 10aligned in the z direction for the 3D image 100 to the backmost two ofthe MRI slices 10 aligned in the z direction for the 3D image 100 toobtain one of the values C₁₋₁₋₁-C_(N-N-N) for each of the stopsW₁₋₁₋₁-W_(N-N-N) of the 3D moving window 102 as seen in FIGS. 26A-26C.

For further elaboration, one of the computation voxels P_(k)

_(l)

_(h) may be in multiple of the stops W_(m)

_(n)

_(u) of the 3D moving window 102 partially overlapping with each otherand one another. In the example, the 3D moving window 102 may have 2×2×2cubes. One of the computation voxels P_(k)

_(l)

_(h) may be in eight of the stops W_(m)

_(n)

_(u) of the 3D moving window 102 partially overlapping with one anotheras seen in FIGS. 26D-26J. FIGS. 26D-26J are schematically views showingtwo of the stops of a 3D moving window partially overlapping with eachother in various manners, wherein one of the computation voxels arewithin said two of the stops of the 3D moving window. Referring to FIG.26D, the computation voxel P_(k)

_(l)

_(h) may be within the two overlapped stops W_(m)

_(n)

_(u) and W_((m)

₁₎

_(n)

_(u) of the 3D moving window shift from each other in the x direction,wherein the number m may be an integer ranger from 1 to (N−1), thenumber n may be an integer ranger from 1 to N and the number u may be aninteger ranger from 1 to N. Referring to FIG. 26E, the computation voxelP_(k)

_(l)

_(h) may be within the two overlapped stops W_(m)

_(n)

_(u) and W_(m)

_((n)

₁₎

_(u) of the 3D moving window shift from each other in the y direction,wherein the number m may be an integer ranger from 1 to N, the number nmay be an integer ranger from 1 to (N−1) and the number u may be aninteger ranger from 1 to N. Referring to FIG. 26F, the computation voxelP_(k)

_(l)

_(h) may be within the two overlapped stops W_(m)

_(n)

_(u) and W_(m)

_(n(u)

₁₎ of the 3D moving window shift from each other in the z direction,wherein the number m may be an integer ranger from 1 to N, the number nmay be an integer ranger from 1 to N and the number u may be an integerranger from 1 to (N−1). Referring to FIG. 26G, the computation voxelP_(k)

_(l)

_(h) may be within the two overlapped stops W_(m)

_(n)

_(u) and W_((m)

₁₎

_((n)

₁₎

_(u) of the 3D moving window shift from each other in the x and ydirections, wherein the number m may be an integer ranger from 1 to(N−1), the number n may be an integer ranger from 1 to (N−1) and thenumber u may be an integer ranger from 1 to N. Referring to FIG. 26H,the computation voxel P_(k)

_(l)

_(h) may be within the two overlapped stops W_(m)

_(n)

_(u) and W_((m)

₁₎

_(n)

_((u)

₁₎ of the 3D moving window shift from each other in the x and zdirections, wherein the number m may be an integer ranger from 1 to(N−1), the number n may be an integer ranger from 1 to N and the numberu may be an integer ranger from 1 to (N−1). Referring to FIG. 26I, thecomputation voxel P_(k)

_(l)

_(h) may be within the two overlapped stops W_(m)

_(n)

_(u) and W_(m)

_((n)

₁₎

_((u)

₁₎ of the 3D moving window shift from each other in the y and zdirections, wherein the number m may be an integer ranger from 1 to N,the number n may be an integer ranger from 1 to (N−1) and the number umay be an integer ranger from 1 to (N−1). Referring to FIG. 26J, thecomputation vowel P_(k)

_(l)

_(h) may be within the two overlapped stops W_(m)

_(n)

_(u) and W_((m)

₁₎

_((n)

₁₎

_((u)

₁₎ of the 3D moving window shift from each other in the x, y and zdirections, wherein the number m may be an integer ranger from 1 to(N−1) the number n may be an integer ranger from 1 to (N−1) and thenumber u may be an integer ranger from 1 to (N−1).

Next, referring to FIGS. 22A, 24, 25 and 26A-26C, in the step S23-2 fordeconvolution operation (E_(d)) one of the values d₁

₁

₁-d_((N)

₁₎

_((N)

₁₎

_((N)

₁₎ for each of the computation voxels P₁

₁

₁-P_((N)

₁₎

_((N)

₁₎

_((N)

₁₎ may be calculated based on the values C_(m)

_(n)

_(u), i.e., C₁

₁

₁-C_(N)

_(N)

_(N), for the respective stops W_(m)

_(n)

_(u), i.e., W₁

₁

₁-W_(N)

_(N)

_(N), each covering said each of the computation voxels P₁

₁

₁-P_((N)

₁₎

_((N)

₁₎

_((N)

₁₎, wherein each of the computation voxels P₁

₁

₁-P_((N)

₁₎

_((N)

₁₎

_((N)

₁₎ has a smaller volume than that of the three-dimensional moving window102.

For more elaboration, with regard to the deconvolution operation(E_(d)), in a step DC1, one of the initial values d₁

₁

₁-d_((N)

₁₎

_((N)

₁₎

_((N)

₁₎ for each of the computation voxels P₁

₁

₁-P_((N)

₁₎

_((N)

₁₎

_((N)

₁₎ may be first calculated or assumed based on an average of the valuesC₁

₁

₁-C_(N)

_(N)

_(N) for the stops W₁

₁

₁-W_(N)

_(N)

_(N) of the moving window 102 overlapping said each of the computationvoxels P₁

₁

₁-P_((N)

₁₎

_((N)

₁₎

_((N)

₁₎. Next, in a step DC2, a guess for each of the stops W₁

₁

₁-W_(N)

_(N)

_(N) of the moving window 102 may be calculated by averaging the initialvalues d₁

₁

₁-d_((N)

₁₎

_((N)

₁₎

_((N)

₁₎ (obtained from the step DC1) for the computation voxels P₁

₁

₁-P_((N)

₁₎

_((N)

₁₎

_((N)

₁₎ inside said each of the stops W₁

₁

₁-W_(N)

_(N)

_(N) of the moving window 102. Next, in a step DC3, one of the guesses(obtained from the step DC2) for each of the stops W₁

₁

₁-W_(N)

_(N)

_(N) of the moving window 102 may be compared with one of the values C₁

₁

₁-C_(N)

_(N)

_(N) for said each of the stops W₁

₁

₁-W_(N)

_(N)

_(N) of the moving window 102 by subtracting said one of the values C₁

₁

₁-C_(N)

_(N)

_(N) for said each of the stops W₁

₁

₁-W_(N)

_(N)

_(N) from said one of the guesses (obtained from the step DC2) for saideach of the stops W₁

₁

₁-W_(N)

_(N)

_(N) to obtain a difference between said one of the values C₁

₁

₁-C_(N)

_(N)

_(N) and said one of the guesses (obtained from the step DC2). Next, ina step DC4, a determination step may be performed to determine whetherthe absolute value of the difference (obtained from the step DC3) isless than or equal to a preset threshold error. If any of the absolutevalues of the differences (obtained from the step DC3) for therespective stops W₁

₁

₁-W_(N)

_(N)

_(N) is greater than the preset threshold error, a step DC5 continues.If the absolute value of the difference (obtained from the step DC3) foreach of the stops W₁

₁

₁-W_(N)

_(N)

_(N) is less than or equal to the preset threshold error, a step DC10continues.

In the step DC5, an error correction factor (ECF) for each of thecomputation voxels P₁

₁

₁-P_((N)

₁₎

_((N)

₁₎

_((N)

₁₎ is calculated by summing error correction contributions from thestops W₁

₁

₁-W_(N)

_(N)

_(N)

of the moving window 102 overlapping said each of the computation voxelsP₁

₁

₁-P_((N)

₁₎

_((N)

₁₎

_((N)

₁₎. For a general example, if the moving window 102 has a size of2-by-2-by-2 computation vowels, there may be neighboring eight of thestops W₁

₁

₁-W_(N)

_(N)

_(N)

of the moving window 102 overlapping one of the computation voxels P₁

₁

₁-P_((N)

₁₎

_((N)

₁₎

_((N)

₁₎. The error correction contribution from each of said neighboringeight of the stops W₁

₁

₁-W_(N)

_(N)

_(N)

to said one of the computation voxels P₁

₁

₁-P_((N)

₁₎

_((N)

₁₎

_((N)

₁₎ may be calculated by multiplying the difference (obtained from thestep DC3) for said each of said neighboring eight of the stops W₁

₁

₁-W_(N)

_(N)

_(N)

by a space ratio of an overlapped space between said one of thecomputation voxels P₁

₁

₁-P_((N)

₁₎

_((N)

₁₎

_((N)

₁₎ and said each of said neighboring eight of the stops W₁

₁

₁-W_(N)

_(N)

_(N) to a space of the moving window 102. Next, in a step DC6, one ofthe initial values d₁

₁

₁-d_((N)

₁₎

_((N)

₁₎

_((N)

₁₎ for each of the computation voxels P₁

₁

₁-P_((N)

₁₎

_((N)

₁₎

_((N)

₁₎ may be updated by subtracting the error correction lector (ECF)(obtained from the step DC5) not said each of the computation voxels P₁

₁

₁-P_((N)

₁₎

_((N)

₁₎

_((N)

₁₎ from the initial value d₁

₁

₁-d_((N)

₁₎

_((N)

₁₎

_((N)

₁₎ for said each of the computation voxels P₁

₁

₁-P_((N)

₁₎

_((N)

₁₎

_((N)

₁₎. Next, in a step DC7, the guess for each of the stops W₁

₁

₁-W_(N)

_(N)

_(N) of the moving window 102 may be updated by averaging the updatedvalues d₁

₁

₁-d_((N)

₁₎

_((N)

₁₎

_((N)

₁₎ (obtained from the step DC6) for the computation voxels P₁

₁

₁-P_((N)

₁₎

_((N)

₁₎

_((N)

₁₎ inside said each of the stops W₁

₁

₁-W_(N)

_(N)

_(N) of the moving window 102. Next, in a step DC8, one of the updatedguesses (obtained from the step DC7) for each of the stops W₁

₁

₁-W_(N)

_(N)

_(N) of the moving window 102 may be compared with one of values C₁

₁

₁-C_(N)

_(N)

_(N) for said each of stops W₁

₁

₁-W_(N)

_(N)

_(N) of the moving window 102 by subtracting said one of the values C₁

₁

₁-C_(N)

_(N)

_(N) for said each of the stops W₁

₁

₁-W_(N)

_(N)

_(N) from said one of the updated guesses (obtained from the step DC7)for said each of the stops W₁

₁

₁-W_(N)

_(N)

_(N) to obtain an updated difference between said one of the values C₁

₁

₁-C_(N)

_(N)

_(N) and said one of the updated guesses. Next. in a step DC9, adetermination step may be performed to determine whether the absolutevalue of the updated difference (obtained from the step DC8) is lessthan or equal to the preset threshold error. If any of the absolutevalues of the updated differences (obtained from the step DC8) for therespective stops W₁

₁

₁-W_(N)

_(N)

_(N) is greater than the preset threshold error, the steps DC5-DC9continues for another iteration. If the absolute value of the updateddifference (obtained from the step DC8) for each of the stops W₁

₁

₁-W_(N)

_(N)

_(N) is less than the preset threshold error, the step DC10 continues.

In the step DC5 in the another iteration, the error correction factor(ECF) for each of the computation voxels P₁

₁

₁-P_((N)

₁₎

_((N)

₁₎

_((N)

₁₎ may be updated by summing updated error correction contributions fromthe stops W₁

₁

₁-W_(N)

_(N)

_(N) of the moving window 102 overlapping said each of the computationvoxels P₁

₁

₁-P_((N)

₁₎

_((N)

₁₎

_((N)

₁₎. For the above general example, the updated error correctioncontribution from said each of said neighboring eight of the stops W₁

₁

₁-W_(N)

_(N)

_(N) to said one of the computation voxels P₁

₁

₁-P_((N)

₁₎

_((N)

₁₎

_((N)

₁₎ may be calculated by multiplying the updated difference (obtainedfrom the step DC8 in the last iteration) for said each of saidneighboring eight of the stops W₁

₁

₁-W_(N)

_(N)

_(N) by the space ratio. Next, in the step DC6 in the another iteration,one of the values d₁

₁

₁-d_((N)

₁₎

_((N)

₁₎

_((N)

₁₎ for each of the computation voxels P₁

₁

₁-P_((N)

₁₎

_((N)

₁₎

_((N)

₁₎ may be updated by subtracting the updated error correction factor(ECF) (obtained from the step DC5 in the current iteration) for saideach of the computation voxels P₁

₁

₁-P_((N)

₁₎

_((N)

₁₎

_((N)

₁₎ from said one of the last updated values d₁

₁

₁-d_((N)

₁₎

_((N)

₁₎

_((N)

₁₎ (obtained from the step DC6 in the last iteration) for said each ofthe computation voxels P₁

₁

₁-P_((N)

₁₎

_((N)

₁₎

_((N)

₁₎. Next, in the step DC7 in the another iteration, the guess for eachof the stops W₁

₁

₁-W_(N)

_(N)

_(N) of the moving window 102 may be updated by averaging the updatedvalues d₁

₁

₁-W_((N)

₁₎

_((N)

₁₎

_((N)

₁₎ (obtained from the step DC6 in the current iteration) for thecomputation voxels P₁

₁

₁-P_((N)

₁₎

_((N)

₁₎

_((N)

₁₎ inside said each of the stops W₁

₁

₁-W_(N)

_(N)

_(N) of the moving window 102. Next, in the step DC8 in the anotheriteration, one of the updated guesses (obtained from the step DC7 in thecurrent iteration) for each of the stops W₁

₁

₁-W_(N)

_(N)

_(N) of the moving window 102 may be compared with one of the values C₁

₁

₁-C_(N)

_(N)

_(N) for said each of the stops W₁

₁

₁-W_(N)

_(N)

_(N) of the moving window 102 by subtracting said one of the values C₁

₁

₁-C_(N)

_(N)

_(N) for said each of the stops W₁

₁

₁-W_(N)

_(N)

_(N) from said one of the updated guesses (obtained from the step DC7 inthe current iteration) for said each of the stops W₁

₁

₁-W_(N)

_(N)

_(N) to obtain an updated difference between said one of the values C₁

₁

₁-C_(N)

_(N)

_(N) and said one of the updated guesses (obtained from the step DC7 inthe current iteration). Next, in the step DC9 in the another iteration,a determination step may be performed to determine whether the absolutevalue of the updated difference (obtained from the DC8 in the currentiteration) is less than or equal to the preset threshold error. If anyof the absolute values of the updated differences (obtained from the DC8in the current iteration) for the respective stops W₁

₁

₁-W_(N)

_(N)

_(N) is greater than the preset threshold error, the above steps DC5-DC9continues for iteration multiple times until the absolute value of theupdated difference (obtained from the DC8 in the current iteration) foreach of the stops W₁

₁

₁-W_(N)

_(N)

_(N) is less than the preset threshold error. If the absolute value ofthe updated difference (obtained from the DC8 in the current iteration)for each of the stops W₁

₁

₁-W_(N)

_(N)

_(N) is less than or equal to the preset threshold error, the step DC10continues.

In the step DC10, one of the updated values d₁

₁

₁-d_((N)

₁₎

_((N)

₁₎

_((N)

₁₎ for each of the computation voxels P₁

₁

₁-P_((N)

₁₎

_((N)

₁₎

_((N)

₁₎ may be determined as an optimal value for said each of thecomputation voxels P₁

₁

₁-P_((N)

₁₎

_((N)

₁₎

_((N)

₁₎, which may be constructed for a 3D computational map,

III-2. Computational Map Derived from Measured Values for Stops ofThree-Dimensional Moving Window

Alternatively, referring to FIGS. 23B, 24, 25 and 26A-26C, in the stepS23-3, a three-dimensional moving window 102 may be applied to a targetspace 100 of a three-dimensional structure, such as biological structureor biopsy tissue, by moving step by step in the target space 100 with ashift equal to a x-direction width X_(fp) of computation voxels P_(k)

_(l)

_(h) of a three-dimensional computational map, moving row by row in thetarget space 100 with a shift equal to a y-direction width Y_(fp) of thecomputation voxels P_(k)

_(l)

_(h) of the three-dimensional computational map and moving plane byplane in the target space 100 with a shift equal to a z-direction widthZ_(fp) of the computation voxels P_(k)

_(l)

_(h) of the three-dimensional computational map, as illustrated in FIGS.26A-26C, to measure a value C_(m)

_(n)

_(u) of an imaging parameter, such as parameter of T1, T2, Ktrans or taufor an MRI parameter or parameter obtained from a wave penetratingdevice configured to generate a wave to penetrate the target space 100,for each stop W_(m)

_(n)

_(u) of the three-dimensional moving window 102. Each neighboring two ofthe stops W_(m)

_(n)

_(u) in a x direction may partially overlap with each other with a shiftequal to a x-direction width X_(fp) of the computation voxels P_(k)

_(l)

_(h) of the three-dimensional computational map. Each neighboring two ofthe stops W_(m)

_(n)

_(u) in a y direction may partially overlap with each other with a shiftequal to a y-direction width Y_(fp) of the computation voxels P_(k)

_(l)

_(h) of the three-dimensional computational map. Each neighboring two ofthe stops W_(m)

_(n)

_(u) in a direction may partially overlap with each other with a shiftequal to a z-direction width Z_(fp) of the computation voxels P_(k)

_(l)

_(h) of the three-dimensional computational map.

One or more of computed tomography (CT) parameters, positron emissiontomography (PET) parameters, single-photon emission computed tomography(SPECT) parameters, micro-PET parameters, micro-SPECT parameters, Ramanparameters, and/or bioluminescence optical (BLO) parameters, ultrasoundparameters, camera-image parameters and/or visible-light-imageparameters may be measured for the value C_(m)

_(n)

_(u) for said each stop W_(m)

_(n)

_(u) of the three-dimensional moving window. The value C_(m)

_(n)

_(u) of the imaging parameter for said each stop W_(m)

_(n)

_(u) of the three-dimensional moving window may be measured fromdetection or analysis instruments, such as camera, microscope (opticalor electronic), endoscope, detectors or spectrometer (visible light,fluorescent light, IR, UV or X-ray), ultrasonic machine or system,magnetic resonance imaging (MRI) machine or system, computed tomography(CT) machine or system, positron emission tomography (PET) machine orsystem, single-photon emission computed tomography (SPECT) machine orsystem, micro-PET machine or system, micro-SPECT machine or system,Raman spectrometer or system, and/or bioluminescence optical (BLO)machine or system, or other machine for obtaining molecular orstructural imaging data.

Next, the step S23-2 as illustrated in FIG. 23A for the third aspectcontinues. Thereby, the algorithm in the second aspect may be employedto transform the value C_(m)

_(n)

_(u) of the imaging parameter for the stops W_(m)

_(n)

_(u) of the three-dimensional moving window into the value d_(k)

_(l)

_(h) of the imaging parameter for the computation voxel P_(k)

_(l)

_(h). The value d_(k)

_(l)

_(h) of the imaging parameter may be calculated as mentioned above inthe third aspect.

III-3. Summary for Third Aspect

Referring to FIGS. 23A and 23, a method for obtaining a value in athree-dimensional computational map for a three-dimensional structure,includes (1) providing, by an imaging system, a first computation voxel,e.g., P_(k)

_(l)

_(h) in FIGS. 26D-26F, which is a three-dimensional unit of thethree-dimensional computational map, having a first dimension X_(fp) ina first direction, e.g., X direction, a second dimension Y_(fp) in asecond direction, e.g., Y direction, and a third dimension Z_(fp) in athird direction, e.g., Z direction; (2) for the step S23-1 or S23-3,obtaining, by the imaging system, a first value, e.g., C₁

₁

₁-C_(N)

_(N)

_(N), of an imaging parameter for each stop, e.g., W₁

₁

₁-W_(N)

_(N)

_(N) in FIGS. 26A-26C, of a three-dimensional moving window 102, whereina first stop, e.g., W_(m)

_(n)

_(u) in FIG. 26D, and a second stop, e.g., W_(m)

_(n)

_(u), W_((m)

₁₎

_(n)

_(u), W_(m)

_((n)

₁₎

_(u) and W_(m)

_(n)

_((n)

₁₎ in FIGS. 26D-26F, of the three-dimensional moving window 102, window102 are partially overlapped and are shifted from each other in thefirst direction, e.g., X direction, by a distance substantially equal tothe firm dimension X_(fp) of the first computation voxel, e.g., P_(k)

_(l)

_(h) in FIGS. 26D-26F, the first stop, e.g., W_(m)

_(n)

_(u) in FIG. 26E, and a third stop, e.g., W_(m)

_((n)

₁₎

_(u) in FIG. 26E, of the stops, e.g., W₁

₁

₁-W_(N)

_(N)

_(N) in FIGS. 26A-26C, of the three-dimensional moving window 102 arepartially overlapped and are shifted from each other in the seconddirection, e.g. Y direction, by a distance substantially equal to thesecond dimension Y_(fp) of the first computation voxel, e.g. P_(k)

_(l)

_(h) in FIGS. 26D-26F, and the first stop, e.g. W_(m)

_(n)

_(u) in FIG. 26F, and a fourth stop, e.g. W_(m)

_(n(u)

₁₎ in FIG. 26F, of the stops, e.g. W₁

₁

₁-W_(N)

_(N)

_(N) in FIGS. 26A-26C, of the three-dimensional moving window 102 arepartially overlapped and are shifted from each other in the thirddirection, e.g. Z direction, by a distance substantially equal to thethird dimension Z_(fp) of the first computation voxel, e.g. P_(k)

_(l)

_(h) in FIGS. 26D-26F; and (3) for the step S23-2, calculating, by theimaging system, a second value, e.g. d_(k)

_(l)

_(h), of the imaging parameter for the first computation voxel, e.g.P_(k)

_(l)

_(h) in FIGS. 26D-26F, based on information associated with the firstvalues, e.g., C_(m)

_(n)

_(u), C_((m)

₁₎

_(n)

_(u), C_(m)

_((n)

₁₎

_(u) and C_(m)

_(n)

_((u)

₁₎, for the first through fourth stops, e.g., W_(m)

_(n)

_(u), W_((m)

₁₎

_(n)

_(u), W_(m)

_((n)

₁₎

_(u) and W_(m)

_(n)

_((u)

₁₎in FIGS. 26D-26F, of the three-dimensional moving window 102.

In this summary for the third aspect, for the step S23-2, saidcalculating the second value, e.g., d_(k)

_(l)

_(h), for the first computation voxel, e.g. P_(k)

_(l)

_(h) in FIGS. 26D-26F, includes (1) calculating, by the imaging system,a first assumed value of the imaging parameter for the first computationvoxel, e.g. P_(k)

_(l)

_(h) in FIGS. 26D-26F, based on information associated with the firstvalues, e.g., C_(m)

_(n)

_(u), C_((m)

₁₎

_(n)

_(u), C_(m)

_((n)

₁₎

_(u) and C_(m)

_(n)

_((u)

₁₎, for the first through fourth stops, e.g., W_(m)

_(n)

_(u), W_((m)

₁₎

_(n)

_(u), W_(m)

_((n)

₁₎

_(u) and W_(m)

_(n)

_((u)

₁₎ in FIGS. 26D-26F, of the three-dimensional moving window 102; (2)calculating, by the imaging system, a second assumed value of theimaging parameter for each voxel of other computation voxels, other thanthe first computation voxel, e.g. P_(k)

_(l)

_(h) in FIGS. 26D-26F, in each of the first through fourth stops, e.g.W_(m)

_(n)

_(u), W_((m)

₁₎

_(n)

_(u), W_(m)

_((n)

₁₎

_(u) and W_(m)

_(n)

_((u)

₁₎ in FIGS. 26D-26F, wherein said calculating the second assumed valuefor a voxel of the other computation voxels in each of the first throughfourth stops, e.g., W_(m)

_(n)

_(u), W_((m)

₁₎

_(n)

_(u), W_(m)

_((n)

₁₎

_(u) and W_(m)

_(n)

_((u)

₁₎ in FIGS. 26D-26F, is based on information associated with the firstvalue for each of the stops of the three-dimensional moving window 102coming the voxel of the other computation voxels; (3) calculating, bythe imaging system, a value guess of the imaging parameter for each stopof the first through fourth stops, e.g., W_(m)

_(n)

_(u), W_((m)

₁₎

_(n)

_(u), W_(m)

_((n)

₁₎

_(u) and W_(m)

_(n)

_((u)

₁₎ in FIGS. 26D-26F, of the three-dimensional moving window 102, whereinsaid calculating the value guess for a stop of the first through fourthstops, e.g., W_(m)

_(n)

_(u), W_((m)

₁₎

_(n)

_(u), W_(m)

_((n)

₁₎

_(u) and W_(m)

_(n)

_((u)

₁₎ in FIGS. 26D-26F, of the three-dimensional moving window 102 is basedon information associated with the first assumed value for the firstcomputation voxel, e.g., P_(k)

_(l)

_(h) in FIGS. 26D-26F, and the second assumed values for the othercomputation voxels in the stop of the first through fourth stops, e.g.,W_(m)

_(n)

_(u), W_((m)

₁₎

_(n)

_(u), W_(m)

_((n)

₁₎

_(u) and W_(m)

_(n)

_((u)

₁₎ in FIGS. 26D-26F; (4) calculating, by the imaging system, adifference between the value guess and the first value, e.g., C_(m)

_(n)

_(u), C_((m)

₁₎

_(n)

_(u), C_(m)

_((n)

₁₎

_(u) and C_(m)

_(n)

_((u)

₁₎, for each of the first through fourth stops, e.g., W_(m)

_(n)

_(u), W_((m)

₁₎

_(n)

_(u), W_(m)

_((n)

₁₎

_(u) and W_(m)

_(n)

_((u)

₁₎ in FIGS. 26D-26F, of the three-dimensional moving window 102; and (5)updating, by the imaging system, the first assumed value for the firstcomputation voxel, e.g. P_(k)

_(l)

_(h) in FIGS. 26D-26F, based on information associated with thedifference for each of the first through fourth stops, e.g., W_(m)

_(n)

_(u), W_((m)

₁₎

_(n)

_(u), W_(m)

_((n)

₁₎

_(u) and W_(m)

_(n)

_((u)

₁₎ in FIGS. 26D-26F, of the three-dimensional moving window 102.

In this summary for the third aspect, for the step S23-2, said updatingthe first assumed value for the first computation voxel, e.g. P_(k)

_(l)

_(h) in FIGS. 26D-26F, further includes: (1) calculating, by the imagingsystem, each of error correction contributions from the first throughfourth stops, e.g., W_(m)

_(n)

_(u), W_((m)

₁₎

_(n)

_(u), W_(m)

_((n)

₁₎

_(u) and W_(m)

_(n)

_((u)

₁₎ in FIGS. 26D-26F, of the three-dimensional moving window 102 to thefirst computation voxel, e.g. P_(k)

_(l)

_(h) in FIGS. 26D-26F, by multiplying the difference for each of thefirst through fourth stops, W_(m)

_(n)

_(u), W_((m)

₁₎

_(n)

_(u), W_(m)

_((n)

₁₎

_(u) and W_(m)

_(n)

_((u)

₁₎ in FIGS. 26D-26F, of the three-dimensional moving window by a ratioof a volume of the first computation voxel, e.g. P_(k)

_(l)

_(h) in FIGS. 26D-26F, to a volume of the three-dimensional movingwindow 102; (2) calculating, by the imaging system, an error correctionfactor (ECF) for the first computation voxel, e.g. P_(k)

_(l)

_(h) in FIGS. 26D-26F, by summing the error correction contributions;(3) subtracting, by the imaging system, the error correction factor(ECF) for the first computation voxel, e.g. P_(k)

_(l)

_(h) in FIGS. 26D-26F, from the first assumed value for the firstcomputation voxel, e.g. P_(k)

_(l)

_(h) in FIGS. 26D-26F.

Fourth Aspect: E Operator for Better Resolution of Probabilities ofEvent in Three-Dimensional Space via Big-Data Engineering Learning IV-1.Probability Map Derived from Measured Values for Original Voxels ofThree-Dimensional Original Map

Referring to FIGS. 22A, 24, 25 and 26A-26C, in the step S22-1 forconvolution operation (E_(c)), a three-dimensional moving window 102 maybe applied to one or a plurality of three-dimensional original mapsregistered to or aligned with each other or one another, wherein the oneor each of the plurality of three-dimensional original maps is providedwith multiple original measured values of a specific one of one or moreimaging parameters, such as parameter of T1, T2, Ktrans or tau for anMRI parameter or parameter obtained from a wave penetrating deviceconfigured to generate a wave to penetrate a target space 100, each forone of its original voxels p

arranged in a three-dimensional array, wherein the one or each of theplurality of three-dimensional original maps is registered to andassociated with and covers the target space 100 for a biologicalstructure, to obtain one or a set of values C_(m)

_(n)

_(u) of the one or more imaging parameters, such as parameters T1, T2and Ktrans for MRI parameters, parameters of T1, T2 and tau for MRIparameters or parameters obtained from the wave penetrating device, foreach stop W_(m)

_(n)

_(u) of the three-dimensional moving window 102. In this case, theoriginal measured values for the respective original voxels p_(i)

_(j)

_(g) of the one or each of the plurality of three-dimensional originalmaps may be associated with an MRI parameter; the one or each of theplurality of three-dimensional original maps may be associated with anMRI slice or a combination of multiple MRI slices registered to oraligned with the target space 100. The one or each of the set of valuesC_(m)

_(n)

_(u) of a specific one of the one or more imaging parameters for saideach stop W_(m)

_(n)

_(u) of the three-dimensional moving window 102 is calculated orobtained based on one or more of the original measured values of thespecific one of the one or more imaging parameters for respective one ormore of the original voxels p_(i)

_(j)

_(g) of the one or one of the plurality or three-dimensional originalmaps, which are covered by or associated with said each stop W_(m)

_(n)

_(u) of the three-dimensional moving window 102. Said each stop W_(m)

_(n)

_(u) of the three-dimensional moving window 102 has a larger volume thanthat of each of the respective one or more of the original voxels p_(i)

_(j)

_(g) of the one or each of the plurality of three-dimensional originalmaps. Each neighboring two of the stops W_(m)

_(n)

_(u) in a x direction may partially overlap with each other with a shiftequal to a x-direction width X_(fp) of computation voxels P_(k)

_(l)

_(h) of a three-dimensional computational map. Each neighboring two ofthe stops W_(m)

_(n)

_(u) in a y direction may partially overlap with each other with a shiftequal to a y-direction width Y_(fp) of the computation voxels P_(k)

_(l)

_(h) of the three-dimensional computational map. Each neighboring two ofthe stops W_(m)

_(n)

_(u) in a direction may partially overlap with each other with a shiftequal to a z-direction width Z_(fp) of the computation voxels P_(k)

_(l)

_(h) of the three-dimensional computational map.

Next, referring to FIG. 22A, in the step S22-2 for big-data engineeringlearning, a learnt resulting parameter, i.e., a probability CL_(m)

_(n)

_(u) or an event, for each stop W_(m)

_(n)

_(u) is calculated or obtained by matching the one or the set of valuesC_(m)

_(n)

_(u) of the one or more imaging parameters for said each stop W_(m)

_(n)

_(u) of the three-dimensional moving window 102 to a classifier such asBayesian classifier. The probability CL_(m)

_(n)

_(u) of the event for each stop W_(m)

_(n)

_(u) of the three-dimensional moving window 102 is independent of avolume of said each stop W_(m)

_(n)

_(u).

Next, referring to FIG. 22A, in the step S22-3 for deconvolutionoperation (E_(d)), a probability of dl_(k)

_(l)

_(h) of the event for each computation voxel P_(k)

_(l)

_(h) of the three-dimensional computational map is iteratively updatedor calculated, as illustrated in steps DL1-DL10 in the fourth aspect,based on one or more of the probabilities CL_(m)

_(n)

_(u) of the event for respective one or more of the stops W_(m)

_(n)

_(u) each covering said each computation voxel P_(k)

_(l)

_(h), wherein said each computation voxel P_(k)

_(l)

_(h) has a smaller volume than that of each of the respective one ormore of the stops W_(m)

_(n)

_(u) of the three-dimensional moving window. The probability dl_(k)

_(l)

_(h) of the event for each computational voxel P_(k)

_(l)

_(h) is independent of a volume of said each computational voxel P_(k)

_(l)

_(h).

In this aspect, engineering learning or machine learning is performedusing the data, dataset or information related to a 3D moving window, orusing the standard size, shape, parameters or format or dimensions ofthe 3D moving window. The description and specification of the steps,processes and methods related to the convolution operator are the sameas in the above. As described and specified above, the convolutionoperator E_(c) transforms the original matrix M_(op) (comprising data,dataset or information (for example, MRI parameters) describing orrepresenting each original or initial voxel in the given 3D space) to aconvolution matrix M_(cw) (comprising averaged data, dataset orinformation (for example, MRI parameters) describing or representingeach stop of 3D moving window in the given 3D space). Through theengineering learning, machine learning or correlation, the data, datasetor information of the elements of M_(cw) may be transformed to a data,dataset or information in a different type, property, item or category.For example, based on big data (accumulated data of correlated clinicalbiopsy analysis data and the measured MRI parameters for patients) andusing (for example) Bayesian inference, the M_(op) (elements of MRIparameters) can be transformed or constructed into a matrix of teamingwindow ML_(w) comprising elements of the probabilities of canceroccurrence. Since the 3D moving window is stepping by the size of afinal or computation voxel, the number of the stops is counted in a 3Darray of final or computation voxels. Each stop of 3D moving window conirises P×Q×R final or computation voxels. The original matrix M_(op)comprises I×J×G voxels and has I×J×G sets in elements or components ofdata, dataset or information. The convolution matrix M_(cw) and thelearning matrix ML_(w) both comprise (K−P+1)×(L−Q+1)×(H−R+1) stops of 3Dmoving window, and has (K−P+1)×(L−Q+1)×(H−R+1) sets or elements orcomponents or data, dataset or information. The E_(c) operatortransforms original matrix M_(op) (comprising I×J×G sets or elements ofdata, dataset or information (for example, MRI parameters) describing orrepresenting each original voxel in the given 3D space) to a convolutionmatrix M_(cw) (comprising (K−P+1)×(L−Q+1)×(H−R+1) sets or elements ofaveraged data, dataset or information (for example, MRI parameters)describing or representing each stop of 3D moving window in the given 3Dspace). The E_(d) operator transforms the convolution matrix M_(cw)(comprising (K−P+1)×(L−Q+1)×(H−R+1) sets or elements of averaged data,dataset or information (for example, MRI parameters) describing orrepresenting each stop of 3D moving window in the given 3D space) to alearning matrix ML_(w) (comprising (K−P+1)×(L−Q+1)×(H−R+1) sets orelements of learned data, dataset or information (for example, theprobability of the cancer occurrence) describing or representing eachstop of 3D moving window in the given 3D space), The engineeringlearning operator (or the machine learning operator), E_(d), can beexpressed as:

E _(d)(M _(cw) , W _(PQR))=ML _(w)

Wherein the 3D moving window comprises P×Q×R final or computation voxelswith P, Q and R in the x, y and z directions, respectively, and thestops W_(m)

_(n)

_(u)'s, are at locations with m, n and u final or computation voxels inthe given 3D space. wherein m=1, 2, 3, . . . , M, n=1, 2, 3, . . . , N,and u=1, 2, 3, . . . , U. The data, dataset or information in or relatedto, or describing each element of the learning matrix ML_(w) for thestop W_(m)

_(n)

_(u) in the given 3D space is an different type, property, category oritem (for example, the probability of the occurrence of a cancer) ascompared to that (for example, MRI parameters) in or related to, ordescribing each element of the convolution matrix M_(cw) for the stopW_(m)

_(n)

_(u) in the same given 3D space. While the data, dataset or informationin or related to, or describing each element of the convolution matrixM_(cw) for the stop W_(m)

_(n)

_(u) in the given 3D space is of a same type, property, category or item(for example, MRI parameters) as compared to that (for example, MRIparameters) in or related to, or describing each element of the originalmatrix M_(op) for the original or initial voxel in the same given 3Dspace. Alternatively, the data, dataset or information related to theoriginal or initial voxels may be, for examples, the IR absorptionimages for a given range of wavenumbers, the Raman scattering images fora given range of wavenumbers, the fluorescent light images for a givenrange of wavenumbers, or the ultrasonic images of a human organ. Asdescribed and specified in the above, the 3D moving window plays a keyrole in the engineering learning operator or algorithm (E operator). Itis defined with some physical, computation, analytical, or statisticalpurposes. Furthermore, the size, volume, shape, parameters or format ofthe 3D moving window is used for the engineering learning or machinelearning. The size, volume, shape, parameters or format of the 3D movingwindow may become a default or standard size, volume or format incollecting, storing, computing, (statistically) analyzing data orinformation, or engineering learning or machine learning. The methods,algorithms or procedures of engineering learning or machine learning ortransforming M_(cw) to ML_(w) may be, for example, using (i) statistics,for example, Baysian inference, (ii) connection or association, forexample, neuro-computing, (iii) Symbolism: for example, induction orinterpretation, (iv) analog, for example, resemblance, (v) evolution,for example, nature processes.

Similar to the deconvolution of M_(cw) described and specified above,the learning matrix ML_(w) can be also deconvoltioned to obtain a finalor computational matrix ML_(dp). The size, volume, shape, parameters orformat of the final or computation voxels are described and specified asin the above. The deconvolution matrix ML_(dp) comprises a final orcomputational data, dataset or information for each final or computationvoxel in the given 3D space. The data, dataset or information in orrelated to, or describing each voxel of the final or computation voxelsin the given 3D space are of the same type, property, category or item(for example, the probability of the occurrence of a cancer) as that(for example, the probability of the occurrence of a cancer) of thelearned data, dataset or information of the elements in ML_(w) for thestops W_(m)

_(n)

_(u) of 3D moving window. The data, dataset or information in or relatedto, or describing each voxel P_(k)

_(l)

_(h) of the final or computation voxels in the given 3D space are of adifferent type, property, category or item (for example, the probabilityof the occurrence of a cancer) as that (for example, MRI parameters) ofthe data, dataset or information of the elements in M_(cw) for the stopsof W_(m)

_(n)

_(u) of moving window. The data, dataset or information in or relatedto, or describing each voxel P_(k)

_(l)

_(h) of the final or computation vowels in the given 3D space are of adifferent type, property, category or item (for example, the probabilityof the occurrence of a cancer) as that (for example, MRI parameters) ofthe data, dataset or information of the elements in M_(op) for theoriginal or initial voxels x_(i)

_(j)

_(g). Alternatively, for examples, based on big data (accumulated dataof correlated clinical biopsy analysis result or data and the measuredIR absorption, Raman scattering data, fluorescent lights or ultrasonicimaging from the correspondent biopsy samples of patients) and using,for example, Bayesian inference, the M_(op) (IR absorption, Ramanscattering data, fluorescent lights or ultrasonic imaging) can betransformed or constructed into a matrix of learning window ML_(w)comprising elements of the probabilities of cancer occurrence.

The data, dataset or information in or related to, or describing eachvoxel P_(k)

_(l)

_(h) of the final or computation voxels can be a number, multiplenumbers, a real number, multiple real numbers, a digitized number (forexample a negative integer, 0, or a positive integer), multipledigitized numbers, a 0 or 1, multiple 0's or 1's, a scalar, multiplescalars, a vector, multiple vectors, or a tensor with degree of order 0,1, 2, . . . , t, where t is an integer. The deconvolution operator E_(d)of the E operator obtains the data, dataset or information for eachfinal or computation voxel by solving a set of linear equations withunknown computation voxel data (dl_(k)

_(l)

_(h)'s) and known data (CL_(m)

_(n)

_(u)'s) of stops of the 3D moving windows. The linear equations can beestablished by equating the data, dataset or information for each stopW_(m)

_(n)

_(u) of moving window to the data, dataset or information averaged overall dl_(k)

_(l)

_(h)'s of the final or computation voxels enclosed by the stop (W_(m)

_(n)

_(u)) of the 3D moving window. The averaging can be done by linearaveraging, Gaussian averaging or Lorentian averaging of dl_(k)

_(l)

_(h)'s.

$\mspace{20mu} {{\frac{1}{P*Q*R}\text{?}\text{?}} = {CL}_{m - n - u}}$?indicates text missing or illegible when filed

Wherein dl_(k)

_(l)

_(h)'s are the data, dataset or information of the final or computationvoxels enclosed by or within the stop W_(m)

_(n)

_(u) of the 3D moving window, wherein k is from k₁ to k₁+P−1, l is froml₁ to l₁+Q−1, h is from h₁ to h_(1+R−)1, and m=1, 2, 3, . . . , K−P+1,n=1, 2, 3, . . . , L−Q+1, u=1, 2, 3, . . . , H−R+1.

There are (K−P+1)×(L−Q+1)×(H−R+3) equations with knows (CL_(m)

_(n)

_(u)'s) and K×L×H unknowns (dl_(k)

_(l)

_(h)'s). The number of unknowns is larger than the number of equations.A method to increase number of knows and decrease number of unknownswill be described below by (1) finding uniform or constant data, datasetor information for the final or computation voxels in a region orregions of uniformity or approximately uniformity within the 3D space ofinterest, and/or (2) finding uniform or constant data, dataset orinformation for the final or computation voxels in a region to regionsof uniformity or approximately uniformity extending from and near oralong the boundary of the 3D space of interest. The set of linearequations can be solved by a computer, device, machine, processor,system or tool iteratively. The initial guess of each of the unknowns(the data, dataset or information of final or computation voxels),dl_(k)

_(l)

_(h), is obtained by averaging over all the stops covering or enclosingthe voxel. The contribution from each enclosing stop calculated by theavolume ratio of the overlapped area (V′_(m)

_(n)

_(u)) to the volume of that stop (V_(m)

_(n)

_(u)), dl_(k)

_(l)

_(h) can be obtained using V_(m)

_(n)

_(u), V′_(m)

_(n)

_(u) and CL_(m)

_(n)

_(u).

$\begin{matrix}{\mspace{79mu} {{\text{?} = {\sum_{m_{1},n_{1},u_{1}}^{m_{2},{n_{2}u_{2}}}{\frac{\text{?}}{v_{m - n - u}}{CL}_{m - n - u}}}}{\text{?}\text{indicates text missing or illegible when filed}}}} & (4)\end{matrix}$

Wherein stops W_(m)

_(n)

_(u)'s covering or enclosing the final or computation voxel P_(k)

_(l)

_(h) have stop indices in from m₁ to m₂, n from n₁ to n₂, and u from u₁to u₂. In the first iteration, we can calculate and obtain the firstdata, dataset or information for each stop of the 3D moving window,CL_(m)

_(n)

_(u)'s, by using initial guess dl_(k)

_(l)

_(h)'s in equation (4). The iteration results in a solutionML_(dp)(K×L×H) when the set of computation voxel data or informationmatch the set of learning window data or information with errors ordifference smaller than or equal to a specified value or number in thesame 3D space. The E_(d) operator can be expressed as:

E _(d)(ML _(w) , W _(PQR))=ML _(dp)

In another aspect of the disclosure, the convolution operator E_(c), thelearning operator E_(l) and the deconvolution operator E_(d) can beperformed in sequence to get the full E operator. The E operatortransform the original matrix M_(op) (comprising elements of data,dataset or information for the I×J×G original or initial voxels and hasI×J×G sets or elements or components of data or information) to thedeconvolution matrix M_(dp) (comprising elements of data, dataset orinformation for the K×L×H voxels and has K×L×H sets or elements orcomponents of data or information) in the same given 3D space, throughthe convolution window matrix M_(cw) (comprising (K−P+1)×(L−Q+1)×(H−R+1)sets or elements or components of data or information of the convolutionwindow stops) and through the learning window matrix ML_(w) (comprising(K−P+1)×(L−Q+1)×(H−R+1) sets or elements or components of data orinformation of the learning window stops). The E operator can beexpressed as

E(M _(op)(I×J×G))=E _(d)(ML _(w)((K−P+1)×(L−Q+1)×(H−R+1)))=E _(d) E_(l)(M _(cw)((K−P+1)×(L−Q+1)×(H−R+1)))=E _(d) E _(l)E_(c)(M_(op)(I×J×G))=ML _(dp)(K×L×H)

In another aspect of the disclosure, this invention discloses the Eoperator in the linear algebra. The linear operations, such as addition(+), subtraction (−), multiplication by a scalar (d) or division by ascalar (/), are performed using the data in information of each stop ofthe 3D moving window, (that is using the elements in the convolutionmatrix M_(cw) or the elements in the learning window ML_(w)), instead ofusing the data or information of the original or initial voxels (that isinstead of using the elements in the convolution matrix M_(op)). The 3Dmoving window is used as a default or standard size, volume,configuration or format for containing and providing data, dataset orinformation for analysis, comparison, computing, engineering learning ormachine learning.

E(a Σ _(s) C _(s) M _(s))=M

Where M, or M is a matrix of the convolution matrix M_(cw), or thelearning matrix ML_(w) and C_(s) are the real numbers, s is an integerfrom 1, 2, 3, . . . , S, with S a positive integer.

Referring to FIGS. 22A, 24, 25 and 26A-26C, in a step S22-1 forconvolution operation (E_(c)), the three-dimensional moving window 102may be applied to the three-dimensional object shown in the 3D image 100as seen in FIG. 24 to obtain one of value sets C_(m)

_(n)

_(u) each containing multiple values for various parameters for each ofstops W_(m)

_(n)

_(u) of the 3D moving window 102, wherein each neighboring two of thestops W_(m)

_(n)

_(u) partially overlap with each other. The 3D moving window 102 mayperform the following steps:

(1) moving step by step with a distance equal to the width X_(fp) of thecube 106 in the x direction (equal to the width of the computationvoxels P_(k)

_(l)

_(h) in the x direction) from a left side of the 3D image 100 to a rightside of the 3D image 100 in a row to obtain one of the value sets C_(m)

_(n)

_(u) for each of the stops W_(m)

_(n)

_(u) of the 3D moving window 102 in the row, for an example, the 3Dmoving window 102 may move step by step by step, in a frontmost two ofthe MRI slices 10 aligned in the z direction for the 3D image 100, witha distance equal to the width X_(fp) of the cube 106 in the x direction(equal to the width of the computation voxels P_(k)

_(l)

_(h) in the x direction) from the left side of the 3D image 100 to theright ride of the 3D image 100 in the topmost row to obtain one of thevalue sets C₁

₁

₁-C_(N)

₁

₁ for each of the stops W₁

₁

₁-W_(N)

₁

₁ of the 3D moving window 102 as seen in FIG. 26A;

(2) moving to the next row of the 3D image 100 with a distance equal tothe width Y_(fp) of the cube 106 in the y direction (equal to the widthof the computation voxels P_(k)

_(l)

_(h) in the y direction) to repeat the step (1) to obtain one of thevalue sets C_(m)

_(n)

_(u) for each of the stops W_(m)

_(n)

_(u) of the 3D moving window 102 in the next bottom row, wherein thesteps (1) and (2) repeat as seen in FIG. 26A until the 3D moving window102 moves to the bottommost row of the 3D image 100 to repeat the step(1) to obtain one of the value sets C_(m)

_(n)

_(u) for each of the stops W_(m)

_(n)

_(u) of the 3D image window 102 in a plane; for the example, the 3Dmoving window 102 may move to the second topmost row with a distanceequal to the width Y_(fp) of the cube 106 in the y direction (equal tothe width of the computation voxels P_(k)

_(l)

_(h) in the y direction) in the frontmost two of the MRI slices 10aligned in the z direction for the 3D image 100 to repeat the step (1)to obtain one of the value sets C₁

₂

₁-C_(N)

₂

₁ for each of the stops W₁

₂

₁-W_(N)

₂

₁ of the 3D moving window 102; the 3D moving window 102 may repeat thestep (1) row by row in the frontmost two of the MRI slices 10 aligned inthe z direction for the 3D image 100 until the 3D moving window 102moves to the bottommost row of the 3D image 100 to obtain one of thevalue sets C₁

₁

₁-C_(N)

_(N)

₁ for each of the stops W₁

₁

₁-W_(N)

_(N)

₁ of the 3D moving window 102 as seen in FIG. 26A;

(3) moving to the next combination of the MRI slices 10 aligned in the zdirection for the 3D image 100 with a distance equal to the width Z_(fp)of the cube 106 in the z direction (equal to the width of thecomputation voxels P_(k)

_(l)

_(h) in the z direction) to repeat the steps (1) and (2) to obtain oneof the value sets C_(m)

_(n)

_(u) for each of the stops W_(m)

_(n)

_(u) of the 3D moving window 102, wherein the steps (1), (2) and (3)repeat until the 3D moving window 102 move to the backmost combinationof the MRI slices 10 aligned in the z direction for the 3D image 100 torepeat the steps (1) and (2) in the backmost combination of the MRIslices 10 aligned in the z direction for the 3D image 100, for theexample, the 3D moving window 102 may repent the steps (1) and (2) planeby plane with a distance equal to the width Z_(fp) of the cube 106 inthe z direction (equal to the width of the computation voxels P_(k)

_(l)

_(h) in the z direction) from the frontmost two of the MRI slices 10aligned in the z direction for the 3D image 100 to the backmost two ofthe MRI slices 10 aligned in the z direction for the 3D image 100 toobtain one of the value sets C₁

₁

₁-C_(N)

_(N)

_(N) for each of the stops W₁

₁

₁-W_(N)

_(N)

_(N) of the 3D moving window 102 as seen in FIGS. 26A-26C.

Each of the value sets C₁

₁

₁-C_(N)

_(N)

_(N) may be a combination of multiple values for various parameters.Each of the value sets C₁

₁

₁-C_(N)

_(N)

_(N) having multiple values for various parameters for one of the stopsW₁

₁

₁-W_(N)

_(N)

_(N) of the 3D moving window 102. In an example for an MRI parameter,each of the widths X_(fp), Y_(fp) and Z_(fp) of the computation voxelsP_(k)

_(l)

_(h) in the x, y and z directions may range from 0.1 to 10 millimeter,and preferably range from 0.5 to 3 millimeters.

The MRI parameters as illustrated in the first aspect may be employedfor the values C_(m)

_(n)

_(u) for the stops W_(m)

_(n)

_(u) of the 3D moving window in the fourth aspect.

The algorithm in the fourth aspect may be employed to transform, via theengineering learning E, the value sets C_(m)

_(n)

_(u) each having the values for various MRI parameters, for therespective stops W_(m)

_(n)

_(u) of the 3D moving window into the computation voxel data dl_(k)

_(l)

_(h), i.e., probabilities of an event, for the respective computationvoxels P_(k)

_(l)

_(h).

Alternatively, each combination of computed tomography (CT) parameters,positron emission tomography (PET) parameters, single-photon emissioncomputed tomography (SPECT) parameters, micro-PET parameters,micro-SPECT parameters, Raman parameters, and/or bioluminescence optical(BLO) parameters, ultrasound parameters, infrared absorbance parameters,camera-image parameters and/or visible-light-image parameters may alsobe taken for a value set C_(m)

_(n)

_(u) for one of the stops W_(m)

_(n)

_(u) of the 3D moving window in the fourth aspect. The data, dataset orinformation C_(m)

_(n)

_(u) for the stops W_(m)

_(n)

_(u) of the 3D moving window in the fourth aspect may be obtained fromdetection or analysis instruments, such as camera, microscope (opticalor electronic), endoscope, detectors or spectrometer (visible light,fluorescent light, IR, UV or X-ray), ultrasonic machine or system,magnetic resonance imaging (MRI) machine or system, computed tomography(CT) machine or system, positron emission tomography (PET) machine orsystem, single-photon emission computed tomography (SPECT) machine orsystem, micro-PET machine or system, micro-SPECT machine or system,Raman spectrometer or system, and/or bioluminescence optical (BLO)machine or system, or other machine for obtaining molecular orstructural imaging data. The algorithm in the fourth aspect may beemployed to transform, via the engineering learning E, the data, datasetor information C_(m)

_(n)

_(u) for the stops W_(m)

_(n)

_(u) of the 3D moving window into the computation voxel data dl_(k)

_(l)

_(h), i.e., probability of an event, for the computation voxel P_(k)

_(l)

_(h).

Next, referring to FIGS. 22A, 24, 25 and 26A-26C, in the step S22-2 forengineering learning, one of probabilities CL₁

₁

₁-C_(N)

_(N)

_(N) of an event for each of the stops W₁

₁

₁-W_(N)

_(N)

_(N) of the 3D moving window 102 as seen in FIGS. 26A-26C may becalculated by matching one of the value sets C₁

₁

₁-C_(N)

_(N)

_(N) for said each of the stops W₁

₁

₁-W_(N)

_(N)

_(N) to a classifier such as Bayesian classifier.

Next, 28, 29, 30A-30C and 31, in a step S22-3 for deconvolutionoperation (E_(d)), one of probabilities dl₁

₁

₁-dl_((N)

₁₎

_((N)

₁₎

_((N)

₁₎ of the event for each of the computation voxels P₁

₁

₁-P_((N)

₁₎

_((N)

₁₎

_((N)

₁₎ may be calculated based on the probabilities CL₁

₁

₁-CL_(N)

_(N)

_(N) of the event for the respective stops W₁

₁

₁-W_(N)

_(N)

_(N) each covering said each of the computation voxels P₁

₁

₁-P_((N)

₁₎

_((N)

₁₎

_((N)

₁₎, wherein each of the computation voxels P₁

₁

₁-P_((N)

₁₎

_((N)

₁₎

_((N)

₁₎ has a smaller volume than that of the three-dimensional moving window102.

For more elaboration, with regard to the deconvolution operation(E_(d)), in a step DL1, one of the original probabilities dl₁

₁

₁-dl_((N)

₁₎

_((N)

₁₎

_((N)

₁₎ for each of the computation voxels P₁

₁

₁-P_((N)

₁₎

_((N)

₁₎

_((N)

₁₎ may be first calculated or assumed based on an average of theprobabilities CL₁

₁

₁-CL_(N)

_(N)

_(N) for the stops W₁

₁

₁

-W_(N)

_(N)

_(N) of the moving window 102 overlapping said each of the computationvoxels P₁

₁

₁-P_((N)

₁₎

_((N)

₁₎

_((N)

₁₎. Next, in a step DL2, a probability guess for each of the stops W₁

₁

₁-W_(N)

_(N)

_(N) of the moving window 102 may be calculated by averaging theoriginal probabilities dl₁

₁

₁-dl_((N)

₁₎

_((N)

₁₎

_((N)

₁₎ (obtained from the step DL1) for the computation voxels P₁

₁

₁-P_((N)

₁₎

_((N)

₁₎

_((N)

₁₎ inside said each of the stops W₁

₁

₁-W_(N)

_(N)

_(N) of the moving window 102. Next, in a step DL3, one of theprobability guesses (obtained from the step DL2) for each of the stopsW₁

₁

₁-W_(N)

_(N)

_(N) of the moving window 102 may be compared with one of theprobabilities CL₁

₁

₁-CL_(N)

_(N)

_(N) for said each of the stops W₁

₁

₁-W_(N)

_(N)

_(N) of the moving window 102 by subtracting said one of theprobabilities CL₁

₁

₁-CL_(N)

_(N)

_(N) for said each of the stops W₁

₁

₁-W_(N)

_(N)

_(N) from said one of the probability guesses (obtained from the stepDL2) for said each of the stops W₁

₁

₁-W_(N)

_(N)

_(N) to obtain difference between said one of the probabilities CL₁

₁

₁-CL_(N)

_(N)

_(N) and said one of the probability guesses (obtained from the stepDL2). Next, in a step DL4, a determination step may be performed todetermine whether the absolute value of the difference (obtained fromthe step DL3) is less than or equal to a preset threshold error. If anyof the absolute values of the differences (obtained from the step DL3)for the respective stops W₁

₁

₁-W_(N)

_(N)

_(N) is greater than the preset threshold error, a step DL5 continues.If the absolute value of the difference (obtained from the step DL3) foreach of the stops W₁

₁

₁-W_(N)

_(N)

_(N) is less than or equal to the preset threshold error, a step DL10continues.

In the step DL5, an error correction factor (ECF) for each of thecomputation voxels P₁

₁

₁-P_((N)

₁₎

_((N)

₁₎

_((N)

₁₎ is calculated by summing error correction contributions from thestops W₁

₁

₁-W_(N)

_(N)

_(N) of the moving window 102 overlapping said each of the computationvoxels P₁

₁

₁-P_((N)

₁₎

_((N)

₁₎

_((N)

₁₎. For a general example, if the moving window 102 has a size of2-by-2by-2 computation voxels, there may be eight of the neighboringstops W₁

₁

₁

-W_(N)

_(N)

_(N) of the moving window 102 overlapping one of the computation voxelsP₁

₁

₁-P_((N)

₁₎

_((N)

₁₎

_((N)

₁₎. The error correction contribution from each of said neighboringeight of the stops W₁

₁

₁-W_(N)

_(N)

_(N) to said one of the computation voxels P₁

₁

₁-P_((N)

₁₎

_((N)

₁₎

_((N)

₁₎ may be calculated by multiplying the difference (obtained from thestep DL3) for said each of said neighboring eight of the stops W₁

₁

₁-W_(N)

_(N)

_(N) by a space ratio of an overlapped space between said one of thecomputation voxels P₁

₁

₁-P_((N)

₁₎

_((N)

₁₎

_((N)

₁₎ and said each of said neighboring eight of the stops W₁

₁

₁-W_(N)

_(N)

_(N) to a space of the moving window 102. Next, in a step DL6, one ofthe original probabilities dl₁

₁

₁-dl_((N)

₁₎

_((N)

₁₎

_((N)

₁₎ for each of the computation voxels P₁

₁

₁-P_((N)

₁₎

_((N)

₁₎

_((N)

₁₎ may be updated by subtracting the error correction factor (ECF)(obtained from the step DL5) for said each of the computation voxels P₁

₁

₁-P_((N)

₁₎

_((N)

₁₎

_((N)

₁₎ from the original probability dl₁

₁

₁-dl_((N)

₁₎

_((N)

₁₎

_((N)

₁₎ for said each of the computation voxels P₁

₁

₁-P_((N)

₁₎

_((N)

₁₎

_((N)

₁₎. Next, in a step DL7, the probability guess for each of the stops W₁

₁

₁-W_(N)

_(N)

_(N) of the moving window 102 may be updated by averaging the updatedprobabilities dl₁

₁

₁-dl_((N)

₁₎

_((N)

₁₎

_((N)

₁₎ (obtained from the step DL6) for the computation voxels P₁

₁

₁-P_((N)

₁₎

_((N)

₁₎

_((N)

₁₎ inside said each of the stops W₁

₁

₁-W_(N)

_(N)

_(N) of the moving window 102. Next, in a step DL8, one of the updatedprobability guesses (obtained from the step DL7) for each of the stopsW₁

₁

₁-W_(N)

_(N)

_(N) of the moving window 102 may be compared with one of theprobabilities CL₁

₁

₁-CL_(N)

_(N)

_(N) for said each of the stops W₁

₁

₁-W_(N)

_(N)

_(N) of the moving window 102 by subtracting said one of theprobabilities CL₁

₁

₁-CL_(N)

_(N)

_(N) for said each of the stops W₁

₁

₁-W_(N)

_(N)

_(N) from said one of the updated probability guesses (obtained from thestep DL7) for said each of the stops W₁

₁

₁-W_(N)

_(N)

_(N) to obtain an updated difference between said one of theprobabilities CL₁

₁

₁-CL_(N)

_(N)

_(N) and said one of the updated probability guesses (obtained from thestep DL7). Next, in a step DL9, a determination step may be performed todetermine whether the absolute value of the updated difference (obtainedfrom the step DL8) is less than or equal to the preset threshold error.If any of the absolute values of the updated differences (obtained fromthe step DL8) for the respective stops W₁

₁

₁-W_(N)

_(N)

_(N) is greater than the preset threshold error, the steps DL5-DL9continues for another iteration. If the absolute value of the updateddifference (obtained from the step DL8) for each of the stops W₁

₁

₁-W_(N)

_(N)

_(N) is less than or equal to the preset threshold error, the step DL10continues.

In the step DL5 in the another iteration, the error correction factor(ECF) for each of the computation voxels P₁

₁

₁-P_((N)

₁₎

_((N)

₁₎

_((N)

₁₎ may be updated by summing updated error correction contributions fromthe stops W₁

₁

₁-W_(N)

_(N)

_(N) of the moving window 102 overlapping said each of the computationvoxels P₁

₁

₁-P_((N)

₁₎

_((N)

₁₎

_((N)

₁₎. For the above general example, the updated error correctioncontribution from said each of said neighboring eight of the stops W₁

₁

₁-W_(N)

_(N)

_(N) to said one of the computation voxels P₁

₁

₁-P_((N)

₁₎

_((N)

₁₎

_((N)

₁₎ may be calculated by multiplying the updated difference (obtainedfrom the step DL8 in the last iteration) for said each of saidneighboring eight of the stops W₁

₁

₁-W_(N)

_(N)

_(N) by the space ratio. Next, in the step DL6 in the another iteration,one of the probabilities dl₁

₁

₁-dl_((N)

₁₎

_((N)

₁₎

_((N)

₁₎ for each of the computation voxels P₁

₁

₁-P_((N)

₁₎

_((N)

₁₎

_((N)

₁₎ may be updated by subtracting the updated error correction factor(ECF) (obtained from the step DL5 in the current iteration) for saideach of the computation voxels P₁

₁

₁-P_((N)

₁₎

_((N)

₁₎

_((N)

₁₎ from said one of the last updated probabilities dl₁

₁

₁-dl_((N)

₁₎

_((N)

₁₎

_((N)

₁₎ (obtained from the step DL6 in the last iteration) for said each ofthe computation voxels P₁

₁

₁-P_((N)

₁₎

_((N)

₁₎

_((N)

₁₎. Next, in the step DL7 in the another iteration, the probabilityguess for each of the stops W₁

₁

₁-W_(N)

_(N)

_(N) of the moving window 102 may be updated by averaging the updatedprobabilities dl₁

₁

₁-dl_((N)

₁₎

_((N)

₁₎

_((N)

₁₎ (obtained from the step DL6 in the current iteration) for thecomputation voxels P₁

₁

₁-P_((N)

₁₎

_((N)

₁₎

_((N)

₁₎ inside said each of the stops W₁

₁

₁-W_(N)

_(N)

_(N) of the moving window 102. Next, in the step DL8 in the anotheriteration, one of the updated probability guesses (obtained from thestep DL7 in the current iteration) for each of the stops W₁

₁

₁-W_(N)

_(N)

_(N) of the moving window 102 may be compared with one of theprobabilities CL₁

₁

₁-CL_(N)

_(N)

_(N) for said each of the stops W₁

₁

₁-W_(N)

_(N)

_(N) of the moving window 102 by subtracting said one of theprobabilities CL₁

₁

₁-CL_(N)

_(N)

_(N) for said each of the stops W₁

₁

₁-W_(N)

_(N)

_(N) from said one of the updated probability guesses (obtained from thestep DL7 in the current iteration) for said each of the stops W₁

₁

₁-W_(N)

_(N)

_(N) to obtain an updated difference between said one of theprobabilities CL₁

₁

₁-CL_(N)

_(N)

_(N) and said one of the updated probability guesses (obtained from thestep DL7 in the current interation). Next, in the step DL9 in theanother iteration, a determination step may be performed to determinewhether the absolute value of the updated difference (obtained from theDL8 in the current iteration) is less than or equal to the presetthreshold error. If any of the absolute values of the updateddifferences (obtained from the DL8 in the current iteration) for therespective stops W₁

₁

₁-W_(N)

_(N)

_(N) is greater than the preset threshold error, the above steps DL5-DL9continues for iteration multiple times until the absolute value of theupdated difference (obtained from the DC8 in the current iteration) foreach of the stops W₁

₁

₁-W_(N)

_(N)

_(N) is less than or equal to the preset threshold error. If theabsolute value of the updated difference (obtained from the DL8 in thecurrent iteration) for each of the stops W₁

₁

₁-W_(N)

_(N)

_(N) is less than for equal to the preset threshold error, the step DL10continues.

In the step DL10, one of the updated probabilities dl₁

₁

₁-dl_((N)

₁₎

_((N)

₁₎

_((N)

₁₎ for each of the computation voxels P₁

₁

₁-P_((N)

₁₎

_((N)

₁₎

_((N)

₁₎ may be determined as an optimal probability for said each of thecomputation voxels P₁

₁

₁-P_((N)

₁₎

_((N)

₁₎

_((N)

₁₎, which may be constructed for a 3D probability map.

An effect of a treatment, such as neoadjuvant chemotherapy or(preoperative) radiation therapy, or a drug for the treatment on asubject (e.g., human or animal) may be evaluated, identified ordetermined by comparing probabilities for two stops of the 3D movingwindows before and after the treatment. Referring to FIG. 19, in thestep S31, a first 3D MRI slice image as seen in FIG. 24 is obtained fromthe subject by the MRI device or system. The first 3D MRI slice image iscomposed of multiple machine-defined original pixels p_(i)

_(j)

_(g) in its field or view (FOV) to show an anatomical space of thesubject, such as prostate or breast. In the step S32, the steps S22-1through S22-3 are performed on the first 3D MRI slice image to obtainfirst probabilities CL_(m)

_(n)

_(u) of an event or data type for stops W_(m)

_(n)

_(u) of the 3D moving window 102 for a computation space of the first 3DMRI slice image. In other words, the first probabilities CL_(m)

_(n)

_(u) of the event or data type for the stops W_(m)

_(n)

_(u) of the 3D moving window 102 on the first 3D MRI slice image for thesubject before the treatment are obtained based on values C_(m)

_(n)

_(u) of the specific MRI parameters for the stops W_(m)

_(n)

_(u) of the 3D moving window 102 on the first 3D MRI slice image tomatch a matching dataset from the established classifier CF or biomarkerlibrary. The values C_(m)

_(n)

_(u) of the specific MRI parameters for the stops W_(m)

_(n)

_(u) of the 3D moving window 102 on the first 3D MRI slice image, forexample, may be obtained from a registered (multi-parametric) imagedataset, e.g., the first 3D MRI slice image and/or different 3Dparameter maps registered to the first 3D MRI slice. The event or datatype, for example, may be prostate cancer, breast cancer, one of Gleasonscores 0 through 10, two or more of Gleason scores 0 through 10 (e.g.,Gleason scores greater than 7), tissue necrosis, or the percentage ofcancer in a specific range from a first percent (e.g., 91 percent) asecond percent (e.g., 100 percent).

Referring to FIG. 19, after the step S31 or S32 is performed, the stepS33 is performed. In the step S33, the subject is given the treatment,such as a drug given intravenously or orally. For certain cancers suchas prostate cancer, the treatment may be the (preoperative) radiationtherapy (or called radiotherapy), a proton beam therapy, a minimallyinvasive treatment (such as ablation or radiation), or an ablationtherapy such as high-intensity focused ultrasound treatment. The(preoperative) radiation therapy for prostate cancer may be performed bya radiotherapy device such as Truebeam or CyberKnife and may usehigh-energy radiation (e.g., gamma rays) to shrink tumors and killcancer cells.

Referring to FIG. 19, in the step S34, after the subject gets orreceives the treatment such as an oral or intravenous drug, a second 3DMRI slice image is obtained from the subject by the MRI device orsystem. The second 3D MRI slice image is obtained from substantially thesame anatomical space of the subject as the first 3D MRI slice image isobtained. The first and second 3D MRI slice images may be composed ofsubstantially the same machine-defined original voxels p_(i)

_(j)

_(g) in the FOV of the MRI machine. In the step S35, the steps S22-1through S22-3 are performed on the second 3D MRI slice image to obtainsecond probabilities CL_(m)

_(n)

_(u) of the event or data type for stops W_(m)

_(n)

_(u) of the moving window 102 for the computation space of the second 3DMRI slice image. In other words, the second probabilities CL_(m)

_(n)

_(u) of the event or data type for the stops W_(m)

_(n)

_(u) of the 3D moving window 102 on the second 3D MRI slice image forthe subject after the treatment are obtained based on values C_(m)

_(n)

_(u) of the specific MRI parameters for the stops W_(m)

_(n)

_(u) of the 3D moving window 102 on the second 3D MRI slice image tomatch the matching dataset from the established classifier CF orbiomarker library. The values C_(m)

_(n)

_(u) of the specific MRI parameters for the stops W_(m)

_(n)

_(u) of the 3D moving window 102 on the second 3D MRI slice image, forexample, may be obtained from a registered (multi-parametric) imagedataset, e.g., the second 3D MRI slice image and/or different 3Dparameter maps registered to the second 3D MRI slice.

The stops W_(m)

_(n)

_(u) of the 3D moving window 102 for the computation space of the first3D MRI slice may substantially correspond to or may be substantiallyaligned with or registered to the stops W_(m)

_(n)

_(u) of the 3D moving window 102 for the computation space of the second3D MRI slice, respectively. Each of the stops W_(m)

_(n)

_(u) of the 3D moving window 102 the computation space of the first 3DMRI slice and the registered or aligned one of the stops W_(m)

_(n)

_(u) of the 3D moving window 102 for the computation space of the second3D MRI slice may cover substantially the same anatomical space of thesubject.

Next, referring to FIG. 19, in the step S36, the first and secondprobabilities CL_(m)

_(n)

_(u) of the event or data type for each aligned or registered pair ofthe stops W_(m)

_(n)

_(u) of the 3D moving window 102 on the first and second 3D MRI sliceimages are subtracted from each other into a corresponding probabilitychange PMC or CCL_(m)

_(n)

_(u) for said each aligned or registered pair of the stops W_(m)

_(n)

_(u) of the 3D moving window 102 on the first and second 3D MRI sliceimages. For example, for each aligned or registered pair of the stopsW_(m)

_(n)

_(u) of the 3D moving window 102 on the first and second 3D MRI sliceimages, the probability change PMC or CCL_(m)

_(n)

_(u) may be obtained by subtracting the first probability CL_(m)

_(n)

_(u) of the event or data type from the second probability CL_(m)

_(n)

_(u) of the event or data type.

Referring tar FIG. 19, in the step S37, the algorithm of the steps S22-1through S22-3 is performed to calculate probability changes PVCs orcdl_(k)

_(l)

_(h) for respective computation voxels P_(k)

_(l)

_(h) based on the probability changes PMCs or CCL_(m)

_(n)

_(u) for the aligned or registered pairs of the stops W_(m)

_(n)

_(u) of the 3D moving window 102 on the first and second 3D MRI sliceimages. The probability changes PVCs or cdl_(k)

_(l)

_(h) for respective computation voxels P_(k)

_(l)

_(h) may compose a 3D probability change map for the event or data type,as described below.

The probability change PVC or cdl_(k)

_(l)

_(h) for each of the computation voxels P_(k)

_(l)

_(h) is assumed by, e.g., averaging the probability changes PMCs orCCL_(m)

_(n)

_(u) of the aligned or registered pairs, of the stops W_(m)

_(n)

_(u) of the 3D moving window 102 on the first and second 3D MRI sliceimages, each overlapping or covering said each of the computation voxelsP_(k)

_(l)

_(h). In the step S12, a probability change guess PG for each aligned orregistered pair of the stops W_(m)

_(n)

_(u) of the 3D moving window 102 on the first and second 3D MRI sliceimages is calculated by, e.g., averaging the probability changes PVCs orcdl_(k)

_(l)

_(h) for all the computation voxels P_(k)

_(l)

_(h) inside said each aligned or registered pair of the stops W_(m)

_(n)

_(u) of the 3D moving window 102 on the first and second 3D MRI sliceimages.

In the step S13, a difference DW between the probability change guess PGand the probability change PMC or CCL_(m)

_(n)

_(u) for each aligned or registered pair of the stops W_(m)

_(n)

_(u) of the 3D moving window 102 on the first and second 3D MRI sliceimages is calculated by, e.g., subtracting the probability change PMC orCCL_(m)

_(n)

_(u) for said each aligned or registered pair of the stops W_(m)

_(n)

_(u) of the 3D moving window 102 on the first and second 3D MRI sliceimages from the probability change guess PG for said each aligned orregistered pair of the stops W_(m)

_(n)

_(u) of the 3D moving window 102 on the first and second 3D MRI sliceimages. In the step S14, an absolute value of the difference DW for eachaligned or registered pair of the stops W_(m)

_(n) of the 3D moving window 102 on the first and second 3D MRI sliceimages is compared with the preset threshold error or value to determinewhether an error, i.e., the absolute value of the difference DW, betweenthe probability change guess PG and the probability change PMC orCCL_(m)

_(n)

_(u) for each aligned or registered pair of the stops W_(m)

_(n)

_(u) of the 3D moving window 102 on the first and second 3D MRI sliceimages is less than or equal to the preset threshold error or value. Ifthe absolute values of the differences DWs for all the aligned orregistered pairs of the stops W_(m)

_(n)

_(u) of the 3D moving window 102 on the first and second 3D MRI sliceimages are determined in the step S14 to be less than or equal to thepreset threshold error or value, the step S16 continues. In the stepS16, the probability changes PVCs or cdl_(k)

_(l)

_(h) for the computation voxels P_(k)

_(l)

_(h) are determined to be optimal, which are called optimal probabilitychanges cdl_(k)

_(l)

_(h) hereinafter, and the optimal probability changes cdl_(k)

_(l)

_(h) of the computation voxels P_(k)

_(l)

_(h) form the 3D probability change map for the event or data type.After the optimal probability changes cdl_(k)

_(l)

_(h) for the computation voxels P_(k)

_(l)

_(h) are obtained in the step S16, the algorithm is completed.

If any one of the absolute values of the differences DWs for all thealigned or registered pairs of the stops W_(m)

_(n)

_(u) of the 3D moving window 102 on the first and second 3D MRI sliceimages is determined in the step S14 to be greater than the presetthreshold error or value, the step S15 continues. In the step S15, theprobability change PVC, i.e., updated cdl_(k)

_(l)

_(h), for each of the computation voxels P_(k)

_(l)

_(h) is updated or adjusted by, e.g., subtracting an error correctionfactor ECF for said each of the computation voxels P_(k)

_(l)

_(h) from the current probability change PVC, i.e., current cdl_(k)

_(l)

_(h), for said each of the computation voxels P_(k)

_(l)

_(h). The error correction factor ECF for each of the computation voxelsP_(k)

_(l)

_(h) is calculated by, e.g., summing error correction contributions fromthe aligned in registered pairs, of the stops W_(m)

_(n) of the 3D moving window 102 on the first and second 3D MRI sliceimages, each covering or overlapping said each of the computation voxelsP_(k)

_(l)

_(h); each of the error correction contributions to said each of thecomputation voxels P_(k)

_(l)

_(h), for example, may be calculated by multiplying the difference DWfor a corresponding one of the aligned or registered pairs of the stopsW_(m)

_(n) of the 3D moving window 102 on be first and second 3D MRI sliceimages by a space ratio of an overlapped space between said each of thecomputation voxels P_(k)

_(l)

_(h) and the corresponding one of the aligned or registered pairs of thestops W_(m)

_(n)

_(u) of the 3D moving window 102 on the first and second 3D MRI sliceimages to a common space of the corresponding one of the aligned orregistered pairs of the stops W_(m)

_(n)

_(u) of the 3D moving window 102 on the first and second 3D MRI sliceimages. After the probability changes PVCs or cdl_(k)

_(l)

_(h) for the computation voxels P_(k)

_(l)

_(h) are updated, the steps S12-S15 are performed repeatedly bawd on theupdated probability changes PVCs, i.e., updated cdl_(k)

_(l)

_(h) for the computation voxels P_(k)

_(l)

_(h) in the step S15, until the absolute values of the differences DWsfor all the aligned or registered pairs of the stops W_(m)

_(n)

_(u) of the 3D moving window 102 on the first and second 3D MRI shoeimages are determined in the step S14 to be less than or equal to thepreset threshold error or value.

The above process uses the 3D moving window 102 in the x, y and zdirections to create a 3D probability change map.

In the step S38, by analyzing the probability change map, the effect ofthe treatment or the drug used in the treatment on the subject may beidentified, determined, or evaluated as effective or ineffective. Basedon the result from the step S38, a doctor can decide or judge whetherthe treatment or the drug should be adjusted or changed. The methoddepicted in the steps S31-S38 can detect responses or progression afterthe treatment or the drugs within less than one week or two weeks,allowing earlier adjustments to the treatment regime.

Alternatively, the effect of a treatment, such as neoadjuvantchemotherapy or (preoperative) radiation therapy, or a drug used in thetreatment on a subject (e.g., human or animal) may be evaluated,identified, or determined in another way as seen not FIG. 20. Referringto FIG. 20, in the step S41, a first 3D MRI slice image is obtained fromthe subject by the MRI device in system. The first 3D MRI slice image iscomposed of multiple machine-defined original voxels p_(i)

_(j)

_(g) in its field of view (FOV) to show an anatomical space of thesubject, such as prostate or breast. In the step S42, the steps S22-1through S22-3 are performed on the first 3D MRI slice image to generatea first 3D probability map composed of first computation voxels P_(k)

_(l)

_(h).

After the step S41 or S42 is performed, the step S43 is performed. Inthe step S43, the subject is given a treatment such as an oral orintravenous drug. For certain cancers such as prostate cancer, thetreatment may be the (preoperative) radiation therapy (or calledradiotherapy), a proton beam therapy, in an ablation therapy such ashigh-intensity focused ultrasound treatment. The (preoperative)radiation therapy for prostate cancer may be performed by a radiotherapydevice such as Truebeam or CyberKnife and may use high-energy radiation(e.g., gamma rays) to shrink tumors and kill cancer cells.

In the step S44, after the subject gets or receives the treatment suchas an oral or intravenous drug, a second 3D MRI slice image is obtainedfrom the subject by the MRI device or system. The second 3D MRI sliceimage is composed of multiple machine-defined original voxels p_(i)

_(j)

_(g) in its FOV to show the same anatomical space of the subject as thefirst 3D MRI slice image shows. In the step S45, the steps S22-1 throughS22-3 are performed on the second 3D MRI slice image to generate asecond 3D probability map composed of second computation voxels P_(k)

_(l)

_(h). Each of the second computation voxels P_(k)

_(l)

_(h) may substantially correspond to or may be substantially alignedwith or registered to one of the first computation voxels P_(k)

_(l)

_(h). The first and second 3D probability maps may be generated for anevent or data type such as prostate cancer, breast cancer, one ofGleason scores 0 through 10, two or more of Gleason scores 0 through 10(e.g., Gleason scores greater than 7), tissue necrosis, or thepercentage of cancer in a specific range from a first percent (e.g., 91percent) to a second percent (e.g., 100 percent).

In the step S46, by subtracting a probability dl_(k)

_(l)

_(h) for each of the first computation voxels P_(k)

_(l)

_(h) from a probability dl_(k)

_(l)

_(h) for the corresponding, registered or aligned one of the secondcomputation voxels P_(k)

_(l)

_(h), a corresponding probability change cdl_(k)

_(l)

_(h) is obtained or calculated. Accordingly, a 3D probability change mapis formed or generated based on the probability changes cdl_(k)

_(l)

_(h). Next, in the step S47, by analyzing the 3D probability change map,the effect of the treatment or the drug used in the treatment on thesubject may be identified, determined, or evaluated as effective orineffective. Based on the result from the step S47, a doctor can decideor judge whether the treatment or the drug should be adjusted orchanged. The method depicted in the steps S41-S47 can detect responsesor progression after the treatment or the drug within less than one weekor two weeks, allowing earlier adjustments to the treatment regime.

IV-2. Probability Map Derived from Measured Values for Stops ofThree-Dimensional Moving Window

Referring to FIGS. 22B, 24, 25 and 26A-26C, in the step S22-4, athree-dimensional moving window 102 may be applied to a target space 100of a three-dimensional structure, such as biological structure or biopsytissue, by moving step by step in the target space 100 with a shiftequal to a x-direction width X_(fp) of computation voxels P_(k)

_(l)

_(h) of a three-dimensional computational map, moving row by row in thetarget space 100 with a shift equal to a y-direction width Y_(fp) of thecomputation voxels P_(k)

_(l)

_(h) of the three-dimensional computational map and moving plane byplane in the target space 100 with a shift equal to a z-direction widthZ_(fp) of the computation voxels P_(k)

_(l)

_(h) of the three-dimensional computational map, as illustrated in FIGS.26A-26C, to measure one or a set of values of one or more imagingparameters, such as parameters of T1, T2, and Ktrans for MRI parameters,parameters of T1, T2 and tau for MRI parameters or parameters obtainedfrom a wave penetrating device, for each stop W_(m)

_(n)

_(u) of the three-dimensional moving window 102. Each neighboring two ofthe stops W_(m)

_(n)

_(u) in a x direction may partially overlap with each other with a shiftequal to a x-direction width X_(fp) of the computation voxels P_(k)

_(l)

_(h) of the three-dimensional computational map. Each neighboring two ofthe stops W_(m)

_(n)

_(u) in a y direction may partially overlap with each other with a shiftequal to a y-direction width Y_(fp) of the computation voxels P_(k)

_(l)

_(h) of the three-dimensional computational map. Each neighboring two ofthe stops W_(m)

_(n)

_(u) in a z direction may partially overlap with each other with a shiftequal to a z-direction width Z_(fp) of the computation voxels P_(k)

_(l)

_(h) of the three-dimensional computational map.

One or more of computed tomography (CT) parameters, positron emissiontomography (PET) parameters, single-photon emission computed tomography(SPECT) parameters, micro-PET parameters, micro-SPECT parameters, Ramanparameters, and/or bioluminescence optical (BLO) parameters, ultrasoundparameters, camera-image parameters and/or visible-light-imageparameters may be measured for the one or the set of values C_(m)

_(n)

_(u) for said each stop W_(m)

_(n)

_(u) of the three-dimensional moving window. The one or the set ofvalues C_(m)

_(n)

_(u) of the one or more imaging parameters for said each stop W_(m)

_(n)

_(u) of the three-dimensional moving window may be measured fromdetection or analysis instruments, such as camera, microscope (opticalor electronic), endoscope, detectors or spectrometer (visible light,fluorescent light, IR, UV or X-ray), ultrasonic machine or system,magnetic resonance imaging (MRI) machine or system, computed tomography(CT) machine or system, positron emission tomography (PET) machine orsystem, single-photon emission computed tomography (SPECT) machine orsystem, micro-PET machine or system, micro-SPECT machine or system,Raman spectrometer or system, and/or bioluminescence optical (BLO)machine or system, or other machine for obtaining molecular orstructural imaging data.

Next, the steps S22-2 and S22-3 as illustrated in FIG. 22A for thefourth aspect continue. Thereby, the algorithm may be employed totransform the one or the set of values C_(m)

_(n)

_(u) of the one or inure imaging parameters for said each stop W_(m)

_(n)

_(u) of the three-dimensional moving window into the probability dl_(k)

_(l)

_(h) of the event for said each computation voxel P_(k)

_(l)

_(h) of the three-dimensional computational map having betterresolution.

IV-3. Summary for Fourth Aspect

Referring to FIGS. 22A and 22B, a method for obtaining a probability ofan event in a three-dimensional probability map for a three-dimensionalstructure, includes: (1) providing, by an imaging system, a firstcomputation voxel, e.g. P_(k)

_(l)

_(h) in FIGS. 26D-26F, which is a three-dimensional unit of thethree-dimensional probability map, having a first dimension X_(fp) in afirst direction, e.g. X direction, a second dimension Y_(fp) in a seconddirection, e.g. Y direction, and a third dimension Z_(fp) in a thirddirection, e.g. Z direction; (2) for the step S22-1 or S22-4, obtaining,by the imaging system, at least one value, e.g. C₁

₁

₁ to C_(N)

_(N)

_(N) of at least one imaging parameter for each stop, e.g. W₁

₁

₁-W_(N)

_(N)

_(N) in FIGS. 26A-26C, of a three-dimensional moving window 102, whereina first stop, e.g. W_(m)

_(n)

_(u) in FIG. 26D, and a second stop, e.g. W_((m)

₁₎

_(n)

_(u) in FIG. 26D, of the stops, e.g. W₁

₁

₁-W_(N)

_(N)

_(N) in FIGS. 26A-26C, of the three-dimensional moving window 102 arepartially overlapped and are shifted from each other in the firstdirection, e.g. X direction, by a distance substantially equal to thefirst dimension X_(fp) of the first computation voxel, e.g. P_(k)

_(l)

_(h) in FIGS. 26D-26F, the first stop, e.g. W_(m)

_(n)

_(u) in FIG. 26E, and a third stop, e.g. W_(m)

_((n)

₁₎

_(u) in FIG. 26E, of the stops, e.g. W₁

₁

₁-W_(N)

_(N)

_(N) in FIGS. 26A-26C, of the three-dimensional moving window 102 arepartially overlapped and are shifted from each other in the seconddirection, e.g. Y direction, by a distance substantially equal to thesecond dimension Y_(fp) of the first computation voxel, e.g. in FIGS.26D-26F, and the first stop, e.g. W_(m)

_(n)

_(u) in FIG. 26F, and a fourth stop, e.g. W_(m)

_(n)

_((u)

₁₎ in FIG. 26F, of the stops, e.g. W₁

₁

₁-W_(N)

_(N)

_(N) in FIGS. 26A-26C, of the three-dimensional moving window 102 arepartially overlapped and are shifted from each other in the thirddirection, e.g. Z direction, by a distance substantially equal to thethird dimension Z_(fp) of the first computation voxel, e.g. P_(k)

_(l)

_(h) in FIGS. 26D-26F; (3) for the step S22-2, matching, by the imagingsystem, the at least one value, e.g. C₁

₁

₁-C_(N)

_(N)

_(N), of the at least one imaging parameter to a classifier to obtain afirst probability, e.g. CL₁

₁

₁ to CL_(N)

_(N)

_(N), of the event for each stop, e.g. W₁

₁

₁-W_(N)

_(N)

_(N) in FIGS. 26A-26C, of the three-dimensional moving window 102, and(4) for the step S22-3, calculating, by the imaging system, a secondprobability, e.g. dl_(k)

_(l)

_(h), of the event for the first computation voxel, e.g. P_(k)

_(l)

_(h) in FIGS. 26D-26F, based on information associated with the firstprobabilities, e.g., CL_(m)

_(n)

_(u), CL_((m)

₁₎

_(n)

_(u), CL_(m)

_((n)

₁₎

_(u) and CL_(m)

_(n)

_((u)

₁₎, of the event for the first through fourth stops, e.g., W_(m)

_(n)

_(u), W_((m)

₁₎

_(n)

_(u), W_(m)

_((n)

₁₎

_(u) and W_(m)

_(n)

_((u)

₁₎ in FIGS. 26D-26F, of the three-dimensional moving window 102.

In this summary for the fourth aspect, for the step S22-3, saidcalculating the second probability, e.g. dl_(k)

_(l)

_(h), of the event for the first computation voxel, e.g. P_(k)

_(l)

_(h) in FIGS. 26D-26F, includes: (1) calculating, by the imaging system,a first assumed probability of the event for the first computationvoxel, e.g. P_(k)

_(l)

_(h) in FIGS. 26D-26F, based on information associated with the firstprobabilities, e.g., CL_(m)

_(n)

_(u), CL_((m)

₁₎

_(n)

_(u), CL_(m)

_((n)

₁₎

_(u) and CL_(m)

_(n)

_((u)

₁₎, of the event for the first through fourth stops, e.g., W_(m)

_(n)

_(u), W_((m)

₁₎

_(n)

_(u), W_(m)

_((n)

₁₎

_(u) and W_(m)

_(n)

_((u)

₁₎ in FIGS. 26D-26F, of the three-dimensional moving window 102; (2)calculating, by the imaging system, a second assumed probability of theevent for each voxel of other computation voxels, other than the firstcomputation voxel, e.g. P_(k)

_(l)

_(h) in FIGS. 26D-26F, in each of the first through stops, e.g., W_(m)

_(n)

_(u), W_((m)

₁₎

_(n)

_(u), W_(m)

_((n)

₁₎

_(u) and W_(m)

_(n)

_((u)

₁₎ in FIGS. 26D-26F, wherein said calculating the second assumedprobability of the event for a voxel of the other computation voxels ineach of the first through fourth stops, e.g., W_(m)

_(n)

_(u), W_((m)

₁₎

_(n)

_(u), W_(m)

_((n)

₁₎

_(u) and W_(m)

_(n)

_((u)

₁₎ in FIGS. 26D-26F, is based on information associated with the firstprobability of the event for each of the stops of the three-dimensionalmoving window 102 covering the voxel of the other computation voxels;(3) calculating, by the imaging system, a probability guess of the eventfor each stop of the first through fourth stops, e.g., W_(m)

_(n)

_(u), W_((m)

₁₎

_(n)

_(u), W_(m)

_((n)

₁₎

_(u) and W_(m)

_(n)

_((u)

₁₎ in FIGS. 26D-26F, of the three-dimensional moving window 102, whereinsaid calculating the probability guess of the event for a stop of thefirst through fourth stops, e.g., W_(m)

_(n)

_(u), W_((m)

₁₎

_(n)

_(u), W_(m)

_((n)

₁₎

_(u) and W_(m)

_(n)

_((u)

₁₎ in FIGS. 26D-26F, of the three-dimensional moving window 102 is basedon information associated with the first assumed probability of theevent for the first computation voxel, e.g., in FIGS. 26D-26F, and thesecond assumed probabilities of the event for the other computationvoxels in the stop of the first through fourth stops, e.g., W_(m)

_(n)

_(u), W_((m)

₁₎

_(n)

_(u), W_(m)

_((n)

₁₎

_(u) and W_(m)

_(n)

_((u)

₁₎ in FIGS. 26D-26F; (4) calculating, by the imaging system, adifference between the probability guess of the event and the firstprobability, e.g., CL_(m)

_(n)

_(u), CL_((m)

₁₎

_(n)

_(u), CL_(m)

_((n)

₁₎

_(u) or CL_(m)

_(n)

_((u)

₁₎, of the event for each of the first through fourth stops, e.g., W_(m)

_(n)

_(u), W_((m)

₁₎

_(n)

_(u), W_(m)

_((n)

₁₎

_(u) and W_(m)

_(n)

_((u)

₁₎ in FIGS. 26D-26F, of the three-dimensional moving window 102; and (5)updating, by the imaging system, the first assumed probability of theevent for the first computation voxel, e.g. P_(k)

_(l)

_(h) in FIGS. 26D-26F, based on information associated with thedifference for each of the first through fourth stops, e.g., W_(m)

_(n)

_(u), W_((m)

₁₎

_(n)

_(u), W_(m)

_((n)

₁₎

_(u) and W_(m)

_(n)

_((u)

₁₎ in FIGS. 26D-26F, of the three-dimensional moving window 102.

In this summary for the fourth aspect, for the step S22-3, said updatingthe first assumed probability or the event for the first computationvoxel, e.g. P_(k)

_(l)

_(h) in FIGS. 26D-26F, further includes: (1) calculating, by the imagingsystem, each of error correction contributions from the first throughfourth stops, e.g., W_(m)

_(n)

_(u), W_((m)

₁₎

_(n)

_(u), W_(m)

_((n)

₁₎

_(u) and W_(m)

_(n)

_((u)

₁₎ in FIGS. 26D-26F, of the three-dimensional moving window 102 to thefirst computation voxel, e.g. P_(k)

_(l)

_(h) in FIGS. 26D-26F, by multiplying the difference for each of thefirst through fourth stops, W_(m)

_(n)

_(u), W_((m)

₁₎

_(n)

_(u), W_(m)

_((n)

₁₎

_(u) and W_(m)

_(n)

_((u)

₁₎ in FIGS. 26D-26F, of the three-dimensional moving window by a ratioof a volume of the first computation voxel, e.g. P_(k)

_(l)

_(h) in FIGS. 26D-26F, to a volume of the three-dimensional movingwindow 102;

(2) calculating, by the imaging system, an error correction factor (ECF)for the first computation voxel, e.g. P_(k)

_(l)

_(h) in FIGS. 26D-26F, by summing the error correction contributions,(3) subtracting, by the imaging system, the error correction factor(ECF) for the first computation voxel, e.g. P_(k)

_(l)

_(h) in FIGS. 26D-26F, from the first assumed probability of the eventfor the first computation voxel, e.g. P_(k)

_(l)

_(h) in FIGS. 26D-26F.

Fifth Aspect: Fixed Value or Probability Set for Computation Pixels orVoxels at Border of Two-dimensional or Three-dimensional ComputationalMap

As mentioned above, in the following equations.

For the first aspect:

$\mspace{20mu} {{\frac{1}{P*Q}\text{?}\text{?}} = {CL}_{m - n}}$?indicates text missing or illegible when filed

For the second aspect:

$\mspace{20mu} {{\frac{1}{P*Q}\text{?}\text{?}} = C_{m - n}}$?indicates text missing or illegible when filed

For the third aspect:

$\mspace{20mu} {{\frac{1}{P*Q*R}\text{?}\text{?}} = C_{m - n - u}}$?indicates text missing or illegible when filed

For the fourth aspect:

$\mspace{20mu} {{\frac{1}{P*Q*R}\text{?}\text{?}} = {CL}_{m - n - u}}$?indicates text missing or illegible when filed

The number of unknowns, i.e., d_(k)

_(l), dl_(k)

_(l), d_(k)

_(l)

_(h) or dl_(k)

_(l)

_(h), may be larger than the number of equations. The above-mentionedmethod to increase number of knows and decrease number of unknowns willbe described below by (1) finding uniform or constant data, dataset orinformation for the final or computation pixels or voxels, i.e., d_(k)

_(l), dl_(k)

_(l), d_(k)

_(l)

_(h) or dl_(k)

_(l)

_(h), in a region, space, regions or spaces of uniformity orapproximately uniformity within the 2D or 3D image of interest, and/or(2) finding uniform or constant data, dataset or information for thefinal or computation pixels or voxels, i.e., d_(k)

_(l), dl_(k)

_(l), d_(k)

_(l)

_(h) or dl_(k)

_(l)

_(h), in a region, space, regions or spaces of uniformity orapproximately uniformity extending from and out of the boundary of the2D or 3D image. The boundary may be a border of a 2D or 3D image for theborder of a biopsy sample. In an example, the data or information for anoutside region at the border of the 2D or 3D image may be the data orinformation of a glass holder, which is uniform and approximate uniformand may be used as the background data or information.

V-1. Computational Map Derived from Measured Values for Original Pixelsof Two-Dimensional Original Map

FIG. 27A illustrates a process of using an E operator to obtain betterresolution of measured values in a two-dimensional region orthree-dimensional space in accordance with an embodiment of the presentapplication FIG. 29A illustrates a schematic view showing a movingwindow for moving across target and outside regions in accordance withan embodiment of the present application. FIGS. 29B-29D are schematicviews showing moving windows at rightmost and bottommost corner of atwo-dimensional computational map in accordance with an embodiment ofthe present application. Referring to FIGS. 27A and 29A, in a step S27-1for convolution operation (E_(c)) a two-dimensional moving window 2 maybe applied to a two-dimensional original map provided with multipleoriginal measured values of an imaging parameter, such as parameter orT1, T2, Ktrans or tau for an MRI parameter or parameter obtained from anoptical image captured by a camera, each for one of its original pixelsp_(i)

_(j) arranged in a two-dimensional array, wherein the two-dimensionaloriginal map is registered to and associated with and covers a targetregion 11 for a biological structure and an outside region 103 for areference or predetermined structure such as glass or metal around thetarget region 11, to obtain a value C₁

₁-C_((M)

₂₎

_((N)

₂₎ of the imaging parameter for each stop W₁

₁-W_((M)

₂₎

_((N)

₂₎ of the two-dimensional moving window 2, wherein some stops W_((M)

₁₎

₁-W_((M)

₂₎

_((N)

₂₎ and W₁

_((N)

₁₎-W_(M)

_((N)

₂₎ of the two-dimensional moving window 2 partially overlap the targetand outside regains 10 and 103. In this case, the original measuredvalues for the respective original pixels p_(i)

_(j) of the two-dimensional original map may be associated with an MRIparameter; the two-dimensional original map may be associated with anMRI slice registered to or aligned with the target region 11. One of thevalues C₁

₁-C_((M)

₂₎

_((N)

₂₎ of the imaging parameter for each stop W₁

₁-W_((M)

₂₎

_((N)

₂₎ of the two-dimensional moving window 2 may be calculated or obtainedbased on one or more of the original measured values of the imagineparameter for respective one or more of the original pixels p_(i)

_(j) of the two-dimensional original map, which are covered by orassociated with said each stop W₁

₁-W_((M)

₂₎

_((N)

₂₎ of the two-dimensional moving window 2. Said each stop W₁

₁-W_((M)

₂₎

_((N)

₂₎ of the two-dimensional moving window 2 has a larger area than that ofeach of the respective one or more of the original pixels p_(i)

_(j) of the two-dimensional original map. Each neighboring two of thestops W₁

₁-W_((M)

₂₎

_((N)

₂₎ in a x direction may partially overlap with each other with a shiftequal to a x-direction width X_(fp) of computation pixels P₁₋₁-P(K

2)

(L

2) of a two-dimensional computational map. Each neighboring two of thestops W₁

₁-W_((M)

₂₎

_((N)

₂₎ in a y direction may partially overlap with each other with a shiftequal to a y-direction width Y_(fp) of the computation pixels P₁

₁-P_((K)

₂₎

_((L)

₂₎ of the two-dimensional computational map.

Referring to FIGS. 27A and 29A-29D, in a step S27-2, a constant value ofthe imaging parameter may be assigned or set for each of the values andd_((K)

₁₎

₁-d_((K)

₂₎

_((L)

₂₎ and d₁

_((L)

₁₎-d_(K)

_((L)

₂₎ of the imaging parameter for each computation pixel P_((K)

₁₎

₁-P_((K)

₂₎

_((L)

₂₎ and P₁

_((L)

₁₎-P_(K)

_((L)

₂₎, which is in the outside region 103, of the two-dimensionalcomputational map since the outside region 103 is a background outsidethe target region 11. In the other words, the values and d_((K)

₁₎

₁-d_((K)

₂₎

_((L)

₂₎ and d₁

_((L)

₁₎-d_(K)

_((L)

₂₎ of the imaging parameter for the respective computation pixels P_((K)

₁₎

₁-P_((K)

₂₎

_((L)

₂₎ and P₁

_((L)

₁₎-P_(K)

_((L)

₂₎ in the outside region 103 become known.

Referring to FIGS. 27A and 29A-29D, in a step S27-3 for deconvolutionoperation (E_(d)), one of the values d₁

₁-d_(K)

_(L) of the imaging parameter for each computation pixel P₁

₁-P_(K)

_(L), which is in the target region 11, of the two-dimensionalcomputational map is iteratively updated or calculated, as illustratedin the steps DC1-DC10 in the second aspect, based on one or more of thevalues C₁

₁-C_((M)

₂₎

_((N)

₂₎ of the imaging parameter for respective one or more of the stops W₁

₁-W_((M)

₂₎

_((N)

₂₎ each covering said each computation pixel P₁

₁-P_(K)

_(L) and/or one or more of the values d_((K)

₁₎

₁-d_((K)

₂₎

_((L)

₂₎ and d₁

_((L)

₁₎-d_(K)

_((L)

₂₎ of the imaging parameter for respective one or more of thecomputation pixels P_((K)

₁₎

₁-P_((K)

₂₎

_((L)

₂₎ and P₁

_((L)

₁₎-P_(K)

_((L)

₂₎ in the outside region 103, each in at least one of the respective oneor more of the stops W₁

₁-W_((M)

₂₎

_((N)

₂₎. Said each computation pixel P₁

₁-P_(K)

_(L) has a smaller area than that of each of the respective one or moreof the stops W₁

₁-W_((M)

₂₎

_((N)

₂₎ of the two-dimensional moving window 2. The values d₁

₁-d_(K)

_(L) of the imaging parameter for the computation pixels P₁

₁-P_(K)

_(L) within the target region 11 are unknown, but the values d_((K)

₁₎

₁-d_((K)

₂₎

_((L)

₂₎ and d₁

_((L)

₁₎-d_(K)

_((L)

₂₎ of the imaging parameter for the computation pixels P_((K)

₁₎

₁-P_((K)

₂₎

_((L)

₂₎ and P₁

_((L)

₁₎-P_(K)

_((L)

₂₎ and in the outside region 103 become known. Since the ratio of thenumber of the known values, including the values C₁

₁-C_((M)

₂₎

_((N)

₂₎, i.e., C₁

₁-C_(K)

_(L), of the imaging parameter for the stops W₁

₁-W_((M)

₂₎

_((N)

₂₎, i.e., W₁

₁-W_(K)

₁, and the values d_((K)

₁₎

₁-d_((K)

₂₎

_((L)

₂₎ and d₁

_((L)

₁₎-d_(K)

_((L)

₂₎ of the imaging parameter for the computation pixels P_((K)

₁₎

₁-P_((K)

₂₎

_((L)

₂₎ and P₁

_((L)

₁₎-P_(K)

_((L)

₂₎ in the outside region 103, to the number of the unknown values d₁

₁-d_(K)

_(L) of the imaging parameter for the computation pixels P₁

₁-P_(K)

_(L) increases, each of the unknown values d₁

₁-d_(K)

_(L) of the imaging parameter for the computation pixels P₁

₁-P_(K)

_(L) in the target region 11 may be shortly updated into an optimalvalue of the imaging parameter by computer iterative computation asmentioned in the second aspect. For example, the value d_(K)

_(L) of the imaging parameter for the computation pixel P_(K)

_(L), which is in the target region 11, of the two-dimensionalcomputational map is iteratively updated or calculated, as illustratedin the steps DC1-DC10 in the second aspect, based on the values C_(M)

_(N)-C_((M)

₂₎

_((N)

₂₎ of the imaging parameter for the respective stops W_(M)

_(N)-W_((M)

₂₎

_((N)

₂₎ each covering the computation pixel P_(K)

_(L) and the values d_((K)

₁₎

_((L)

₂₎, d_((K)

₂₎

_((L)

₂₎, d_((K)

₁₎

_((L)

₁₎, d_((K)

₂₎

_((L)

₁₎-d_((K)

₁₎

_(L), d_((K)

₂₎

_(L), d_((K)

₂₎

_((L)

₁₎, d_((K)

₁₎

_((L)

₁₎, d_(K)

_((L)

₁₎, d_((K)

₁₎

_((L)

₁₎, d_((K)

₂₎

_((L)

_(1), d) _((K)

₂₎

_((L)

₂₎, d_((K)

₁₎

_((L)

₂₎, d_(K)

_((L)

₂₎, d_((K)

₁₎

_((L)

₂₎ and d_((K)

₂₎

_((L)

₂₎ of the imaging parameter for the respective computation pixels P_((K)

₁₎

_((L)

₂₎, P_((K)

₂₎

_((L)

₂₎, P_((K)

₁₎

_((L)

₁₎, P_((K)

₂₎

_((L)

₁₎, P_((K)

₁₎

_(L), P_((K)

₂₎

_(L), P_((K)

₂₎

_((L)

₁₎, P_((K)

₁₎

_((L)

₁₎, P_(K)

_((L)

₁₎, P_((K)

₁₎

_((L)

₁₎, P_((K)

₂₎

_((L)

₁₎, P_((K)

₂₎

_((L)

₂₎, P_((K)

₁₎

_((L)

₂₎, P_(K)

_((L)

₂₎, P_((K)

₁₎

_((L)

₂₎ and P_((K)

₂₎

_((L)

₂₎ in the outside region 103, each in at least one of the stops W_(M)

_(N)-W_((M)

₂₎

_((N)

₂₎.

Alternatively, referring to FIGS. 29A and 30A-30D, one of the values d₁

₁-d_(K)

_(L) of the imaging parameter for each of the computation pixels P₁

₁-P_(K)

_(L) within the target region 11 may be solved from the value d_(K)

_(L) of the imaging parameter for the computation pixel P_(K)

_(L) at a corner of the target region 11 between the right-side andbottom-side borders of the target region 11, as described in thefollowing method. At the beginning, the value d_(K)

_(L) of the imaging parameter for the computation pixel P_(K)

_(L) at the corner of the target region 11 between the right-side andbottom-side borders of the target region 11 may be first calculated.Next, the values d₁

₁-d_((K)

₁₎

_((L)

₁₎, d_(K)

₁-d_(K)

_((L)

₁₎ and d₁

₁-d_(K)

_(L))

₁ of the imaging parameter for the respective computation pixels P₁

₁-P_((K)

₁₎

_((L)

₁₎, P_(K)

₁-P_(K)

_((L)

_(1) and P) ₁

₁-P_((K)

₁₎

_(L) in the target region 11 may be solved pixel by pixel from one ofthe values d_(k)

_(l) of the imaging parameter for one of the computation pixels P_(k)

_(l) to another value d

of the imaging parameter for another computation pixel P

shifted from said one of the computation pixels P_(k)

_(l) in the leftward direction; the values d₁

₁-d_((K)

₁₎

_((L)

₁₎, d_(K)

₁-d_(K)

_((L)

₁₎ and d₁

₁-d_((K)

₁₎

_(L) of the imaging parameter for the respective computation pixels P₁

₁-P_((K)

₁₎

_((L)

_(1), P) _(K)

₁-P_(K)

_((L)

₁₎ and P₁

₁-P_((K)

₁₎

_(L) in the target region 11 may be solved pixel by pixel from one ofthe values d_(k)

_(l)of the imaging parameter for one of the computation pixels P_(k)

_(l) to another value d

of the imaging parameter for another computation pixel P_(k)

₍

₎ shifted from said one of the computation pixels P_(k)

_(l) in the upward direction.

For more elaboration, referring to FIG. 30B, the value d_(K)

_(L) of the imaging parameter for the computation pixel P_(K)

_(L) may be solved hosed on the value C_((M)

₂₎

_((N)

₂₎ of the imaging parameter for the stop W_((M)

₂₎

_((N)

₂₎ of the moving window 2 and the values d(K

1)

L, d_((K)

₂₎

_(L), d₍

_((L)

₁₎, d_((K)

₁₎

_((L)

₁₎d_((K)

₂₎

_((L)

₁₎, d_(K)

_((L)

₂₎, d_((K)

₁₎

_((L)

_(2) and d) _((K)

₂₎

_((L)

₂₎ of the imaging parameter for the respective pixels P_((K)

₁₎

_(l), P_((K)

₂₎

_(L), P_(K)

_((L)

₁₎, P_((K)

₁₎

_((L)

₁₎, P_((K)

₂₎

_()L)

₁₎, P_(K)

_((L)

₂₎, P_((K)

₁₎

_((L)

₂₎ and P_((K)

₂₎

_((L)

₂₎ within the stop W_((M)

₂₎

_((N)

₂₎. Since the value C_((M)

₂₎

_((N)

₂₎ of the imaging parameter for the stop W_((M)

₂₎

_((N)

₂₎ of the moving window 2 and the values d_((K)

₁₎

₁, d_((K)

₂₎

_(L), d_((K)

_((L)

₁₎, d_((K)

₁₎

_((L)

₁₎, d_((K)

₂₎

_((L)

₁₎, d_(K)

_((L)

₂₎, d_((K)

₁₎

_((L)

₂₎ and d_((K)

₂₎

_((L)

₂₎ of the imaging parameter for the respective pixels P_((K)

₁₎

_(L), P_((K)

₂₎

_(L), P_(K)

_((L)

₁₎, P_((K)

₁₎

_((L)

₁₎, P_((K)

₂₎

_()L)

₁₎, P_(K)

_((L)

₂₎, P_((K)

₁₎

_((L)

₂₎ and P_((K)

₂₎

_((L)

₂₎ are known, the unknown value d_(K)

_(L) of the imaging parameter for the computation pixel P_(K)

_(L) may be solved.

After the value d_(K)

_(L) of the imaging parameter for the computation pixel P_(K)

_(L) is solved, the values d_((K)

₁₎

_(L) and d_(K)

_((L)

₁₎ of the imaging parameter for the respective pixels P_((K)

₁₎

_(L) and P_(K)

_((L)

₁₎ next to the computation pixel P_(K)

_(L) at it left and upper sides respectively may be solved. Referring toFIG. 30C, the value d_((K)

₁₎

_(L) of the imaging parameter for the computation pixel P_((K)

₁₎

_(L) may be solved based on the value C_((M)

₁₎

_((N)

₂₎ of the imaging parameter for the stop W_((M)

₁₎

_((N)

₂₎ of the moving window 2 and the values d_(K)

_(L), d_((K)

₁₎

_(L, d) _((K)

₁₎

_((L)

₁₎, d_(K)

_((L)

₁₎, d_((K)

₁₎

_((L)

₁₎, d_((K)

₁₎

_((L)

₂₎, d_(K)

_((L)

₂₎ and d_((K)

₁₎

_((L)

₂₎ of the imaging parameter for the respective pixels P_(K)

_(L), P_((K)

₁₎

_(L), P_((K)

₁₎

_((L)

₁₎, P_(K)

_((L)

₁₎, P_((K)

₁₎

_((L)

₁₎, P_((K)

₁₎

_((L)

₂₎, P_(K)

_((L)

₂₎ and P_((K)

₁₎

_(L)

₂₎ within the stop W_((M)

₁₎

_((N)

₂₎. Since the value C_((M)

₁₎

_((N)

₂₎ of the imaging parameter for the stop W_((M)

₁₎

_((N)

₂of the moving window 2 and the values d_(K)

_(L), d_((K)

₁₎

_(L, d) _((K)

₁₎

_((L)

₁₎, d_(K)

_((L)

₁₎, d_((K)

₁₎

_((L)

₁₎, d_((K)

₁₎

_((L)

₂₎, d_(K)

_((L)

₂₎ and d_((K)

₁₎

_((L)

₂₎ of the imaging parameter for the respective pixels P_(K)

_(L), P_((K)

₁₎

_(L), P_((K)

₁₎

_((L)

₁₎, P_(K)

_((L)

₁₎, P_((K)

₁₎

_((L)

₁₎, P_((K)

₁₎

_((L)

₂₎, P_(K)

_((L)

₂₎ and P_((K)

₁₎

_(L)

₂₎ are known, the unknown value d_((K)

₁₎

_(L) of the imaging parameter for the computation pixel P_((K)

₁₎

_(L) may be solved.

Referring to FIG. 30D, the value d_(K)

_((L)

₁₎ of the imaging parameter for the computation pixel P_(K)

_((L)

₁₎ may be solved based on the value C_((M)

₂₎

_((N)

₁₎ of the imaging parameter for the stop W_((M)

₂₎

_((N)

₁₎ of the moving window 2 and the values d₍ _(K)

₁₎

_((L)

₁₎, d_((K)

₂₎

_((L)

₁₎, d_(K)

_(L), d_((K)

₁₎

_(L), d_((K)

₂₎

_(L), d_(K)

_((L)

₁₎, d_((K)

₁₎

_((L)

₁₎ and d_((K)

₂₎

_((L)

₁₎ of the imaging parameter for the respective pixels P_((K)

₁₎

_((L)

₁₎, P_((K)

₂₎

_((L)

₁₎, P_(K)

_(L), P_((K)

₁₎

_(L), P_((K)

₂₎

_(L), P_(K)

_((L)

₁₎, P_(K)

₁₎

_((L)

₁₎ and P_((K)

₂₎

_((L)

₁₎ within the stop W_((M)

₂₎

_((N)

₁₎. Since the value C_((M)

₂₎

_((N)

₁₎ of the imaging parameter for the stop W_((M)

₂₎

_((L)

₁₎ of the moving window 2 and the values d_((K)

₁₎

_((L)

₁₎, d_((K)

₂₎

_((L)

₁₎, d_(K)

_(L), d_((K)

₁₎

_(L), d_((K)

₂₎

_(L), d_(K)

_((L)

₁₎, d_((K)

₁₎

_((L)

₁₎ and d_((K)

₂₎

_((L)

₁₎ of the imaging parameter for the respective pixels P_((K)

₁₎

_((L)

₁₎, P_((K)

₂₎

_()L)

₁₎, P_(K)

_(L), P_((K)

₁₎

_(L), P_((K)

₂₎

_(L), P_(K)

_((L)

₁₎, P_((K)

₁₎

_((L)

₁₎ and P_((K)

₂₎

_((L)

₁₎ are known, the unknown value d_(K)

_((L)

₁₎ of the imaging parameter for the computation pixel P_(K)

_((L)

₁₎ may be solved.

After the values d_(K)

_(L), d_((K)

₁₎

_(L) and d_(K)

_((L)

₁₎ of the imaging parameter for the respective pixels P_(K)

_(L), P_((K)

₁₎

_(L) and P_(K)

_((L)

₁₎ are solved, the unknown values d_((K)

₂₎

_(L), d_((K)

₁₎

_((L)

₁₎ and d_(K)

_((L)

₂₎ of the imaging parameter for the respective pixels P_((K)

₂₎

_(L), P_((K)

₁₎

_((L)

₁₎ and P_(K)

_((L)

₂₎ next to the computation pixel P_((K)

₁₎

_(L) or P_(K)

_((L)

₁₎ may be solved. Thereby, the unknown values d_(k)

_(l) of the imaging parameter for the computation pixels P_(k)

_(l) in the target region 11 may be solved pixel by pixel in leftward orupward direction until the value d₁

₁ of the imaging parameter for the computation pixel P₁

₁ is solved. Accordingly, all of the values d₁

₁-d_(K)

_(L) of the imaging parameter for the computation pixels P₁

₁-P_(K)

_(L) within the target region 11 may be solved.

V-2. Computational Map Derived from Measured Values for Stops ofTwo-Dimensional Moving Window

Alternatively, FIG. 27B illustrates a process of using an E operator toobtain better resolution of values for pixels or voxels of atwo-dimensional or three-dimensional map in accordance with anotherembodiment of the present application. The process as illustrated inFIG. 27B is the same as that as illustrated in FIG. 27A except that thestep S27-1 is replaced with a step S27-4. Referring to FIGS. 27B and29A-29D, in the step S27-4, a two-dimensional moving window 2 may beapplied to a two-dimensional region divided into a target region 11 andan outside region 103 around the target region 11 by moving step by stepon the two-dimensional region with a shift equal to a x-direction widthX_(fp) of computation pixels P₁

₁-P_((K)

₂₎

_((L)

₂₎ of a two-dimensional computational map and moving row by row on thetwo-dimensional region with a shift equal to a y-direction width Y_(fp)of the computation pixels P₁

₁-P_((K)

₂₎

_((L)

₂₎ of the two-dimensional computational map to measure a value C₁

₁-C_((M)

₂₎

_((N)

₂₎ of an imaging parameter, such as parameter of T1, T2, Ktrans or taufor an MRI parameter or parameter obtained from an optical imagecaptured by a camera, for each stop W₁

₁-W_((M)

₂₎

_((N)

₂₎ of the two-dimensional moving window 2, wherein some stops W_((M)

₁₎

_(L)-W_((M)

₂₎

_((N)

₂₎ and W_(L)

_((N)

₁₎-W_(M)

_((N)

₂₎ of two-dimensional moving window 2 partially overlap the target andoutside regions 10 and 103. Each neighboring two of the stops W₁

₁-W_((M)

₂₎

_((N)

_(2) in a x direction may partially overlap with each other with a shift equal to a x-direction width X)_(fp), of the computation pixels P₁

₁-P_((K)

₂₎

_((L)

₂₎ of the two-dimensional computational map. Each neighboring two of thestops W₁

₁-W_((M)

₂₎

_((N)

₂₎ in a y direction may partially overlap with each other with a shiftequal to a y-direction width Y_(fp) of the computation pixels P₁

₁-P_((K)

₂₎

_((L)

₂₎ of the two-dimensional computational map.

One or more of computed tomography (CT) parameters, positron emissiontomography (PET) parameters, single-photon emission computed tomography(SPECT) parameters, micro-PET parameters, micro-SPECT parameters, Ramanparameters, and/or bioluminescence optical (BLO) parameters, ultrasoundparameters, camera-image parameters and/or visible-light-imageparameters may be measured for the value C₁

₁-C_((M)

₂₎

_((L)

₂₎ of the imaging parameter for said each stop W₁

₁-W_((M)

₂₎

_((N)

₂₎ of the two-dimensional moving window. The value C₁

₁-C_((M)

₂₎

_((N)

₂₎ of the imaging parameter for said each stop W₁

₁-W_((M)

₂₎

_((N)

₂₎ of the two-dimensional moving window may be measured from detectionor analysts instruments, such as camera, microscope (optical orelectronic), endoscope, detectors or spectrometer (visible light,fluorescent light, IR, UV or X-ray), ultrasonic machine or system,magnetic resonance imaging (MRI) machine or system, computed tomography(CT) machine or system, positron emission tomography (PET) machine orsystem, single-photon emission computed tomography (SPECT) machine insystem, micro-PET machine or system, micro-SPECT machine or system,Raman spectrometer or system, and/or bioluminescence optical (BLO)machine or system, or other machine for obtaining molecular orstructural imaging data

In an example, referring to FIGS. 27B and 29A, a biopsy tissue may befixed on a glass slide 104. The biopsy tissue may be spread on thetarget region 11 and may be captured by a camera or microscope. Theoutside region 103 may be provided by a portion of the glass slide 104around the biopsy tissue in the target region 11. The two-dimensionalmoving window 2 may move step by step with a shift equal to ax-direction width X_(fp) of the computation pixels P₁

₁-P_((K)

₂₎

_((L)

₂₎ of the two-dimensional computational map and move row by row with ashift equal to a y-direction width Y_(fp) of the computation pixels P₁

₁-P_((K)

₂₎

_((L)

₂₎ of the two-dimensional computational map to move across the targetand outside regions 11 and 103 to measure a value C₁

₁-C_((M)

₂₎

_((N)

₂₎ of an infrared absorbance parameter at a specific spectrum for eachstop W₁

₁-W_((M)

₂₎

_((N)

₂₎ of the two-dimensional moving window 2.

Next, referring to FIG. 27B, the steps S27-2 and S27-3 as illustrated inFIGS. 27A and 29A-29D continues.

V-3. Computational Map Derived from Measured Values for Original Voxelsof Three-Dimensional Original Map

Alternatively, FIGS. 30A and 30B illustrate schematic views showing amoving window for moving across target and outside spaces of athree-dimensional original map in accordance with an embodiment of thepresent application. Referring to FIGS. 27A, 30A and 30B, in the stepS27-1 for the convolution operation, the three-dimensional moving window102 as seen in FIG. 25 may be applied to the three-dimensional originalmap provided with multiple original measured values of an imagingparameter, such as parameter of T1, T2, Ktrans or tau for an MRIparameter or parameter obtained from a wave penetrating deviceconfigured to generate a wave to penetrate a target space 100, each forone of its original voxels p_(i)

_(j)

_(g) arranged in a three-dimensional array, wherein thethree-dimensional original map is registered to and associated with andcovers the target space 100 for a biological structure and a outsidespace 103 for a reference or predetermined structure such as glass ormetal around the target space 100, to obtain a value C₁

₁

₁--C_((N)

₁₎

_((N)

₁₎

_((N)

₁₎ of the imaging parameter for each stop W₁

₁

₁-W_((N)

₁₎

_((N)

₁₎

_((N)

₁₎ of the three-dimensional moving window 102, wherein some stops W₁

₁

_((N)

₁₎-W_((N)

₁₎

_((N)

₁₎

_((N)

₁₎, W₁

_((N)

₁₎

₁-W_((N)

₁₎

_((N)

₁₎

_((N)

₁₎ and W_((N)

₁₎

₁

₁-W_((N)

₁₎

_((N)

₁₎

_((N)

₁₎ of the three-dimensional moving window 102 partially overlap thetarget and outside spaces 100 and 103. In this case, the originalmeasured values for the respective original voxels p_(i)

_(j)

_(g) of the three-dimensional original map may be associated with an MRIparameter; the three-dimensional original map may be associated with acombination of multiple MRI slices registered to or aligned with acombination of the target and outside spaces 100 and 103. One of thevalues C₁

₁

₁-C_((N)

₁₎

_((N)

₁₎

_((N)

₁₎ of the imaging parameter for each stop W₁

₁

₁-W_((N)

₁₎

_((N)

₁₎

_((N)

₁₎ of the three-dimensional moving window 102 may be calculated orobtained based on one or more of the original measured values of theimaging parameter for respective one or more of the original pixelsp_(i)

_(j)

_(g) of the three-dimensional original map, which are covered by orassociated with said each stop W₁

₁

₁-W_((N)

₁₎

_((N)

₁₎

_((N)

₁₎ of the three-dimensional moving window 102. Said each stop W₁

₁

₁-W_((N)

₁₎

_((N)

₁₎

_((N)

₁₎ of the three-dimensional moving window 102 has a larger volume thanthat of each of the respective one or more of the original voxels p_(i)

_(j)

_(g) of the three-dimensional original map. Each neighboring two of thestops W₁

₁

₁-W_((N)

₁₎

_((N)

₁₎

_((N)

₁₎ in a x direction may partially overlap with each other with a shiftequal to a x-direction width X_(fp) of the computation voxels P_(k)

_(l)

_(h) of a three-dimensional computational map. Each neighboring two ofthe stops W₁

₁

₁-W_((N)

₁₎

_((N)

₁₎

_((N)

₁₎ in a y direction may partially overlap with each other with a shiftequal to a y-direction width Y_(fp) of the computation voxels P_(k)

_(l)

_(h) of the three-dimensional computational map. Each neighboring two ofthe stops W₁

₁

₁-W_((N)

₁₎

_((N)

₁₎

_((N)

₁₎ in a z direction may partially overlap with each other with a shiftequal to a z-direction width Z_(fp) of the computation voxels P_(k)

_(l)

_(h) of the three-dimensional computational map. The step S27-1 may bereferred to the description as illustrated in FIGS. 26A-26C in the thirdaspect.

For example, referring to FIGS. 30A and 30B, the moving window 102 maymove in the path mentioned as follows to obtain the values C₁

₁

₁-C_((N)

₁₎

_((N)

₁₎

_((N)

₁₎ of the imaging parameter for the respective stops W_((N)

₁₎

_((N)

₁₎

_((N)

₁₎ of the three-dimensional moving window 102:

(1) moving step by step with a distance or shift equal to the widthX_(fp) of the cube 106, i.e., computation voxel, in the x direction froma left side of the three-dimensional original map to a right side of thethree-dimensional original map in a row and across the target andoutside spaces 100 and 103 to obtain one of the values C_(m)

_(n)

_(u) of the imaging parameter for each of the stops W_(m)

_(n)

_(u) of the three-dimensional moving window 102 in the row; for anexample, the three-dimensional moving window 102 may move step by step,in frontmost two of the MRI slices 10 aligned in the z direction for thethree-dimensional original map, with a distance or shift equal to thewidth X_(fp) of the cube 106, i.e., computation voxel, in the xdirection from the left side of the three-dimensional original map tothe right side of the three-dimensional original map in the topmost rowto obtain one of the values C₁

₁

₁-C_((N)

₁₎

₁

₁ of the imaging parameter for each of the stops W₁

₁

₁-W_((N)

₁₎

₁

₁ of the three-dimensional moving window 102 as seen in FIG. 31A, eachof the stops W₁

₁

₁-W_(N)

₁

₁ is in the target space 100, but the stop W_((N)

₁₎

₁

₁ has a left portion in the target space 100 and a right portion in theoutside space 103:

(2) moving to the next row of the three-dimensional original map with adistance or shift equal to the width Y_(fp) of the cube 106, i.e.,computation voxel, in the y direction to repeat the step (1) in a row ofthe three-dimensional original map to obtain one of the values C_(m)

_(n)

_(u) of the imaging parameter for each of stops W_(m)

_(n)

_(u) of the three-dimensional moving window 102 in the next bottom row,wherein the steps (1) and (2) repeat in a plane of the three-dimensionaloriginal map until the three-dimensional moving window 102 move to thebottommost row of the three-dimensional original map to repeat the step(1) in the bottommost row of the three-dimensional original map toobtain one of the values C_(m)

_(n)

_(u) of the imaging parameter for each of the stops W_(m)

_(n)

_(u) of the three-dimensional moving window 102 in a plane; for theexample, the three-dimensional moving window 102 may move to the secondtopmost row with a distance or shift equal to the width Y_(fp) of thecube 106, i.e., computation voxel, in the y direction in the frontmosttwo of the MRI slices 10 aligned in the z direction for thethree-dimensional original map to repeat the step (1) in a row of thethree-dimensional original map to obtain one of the values C₁

₂

₁-C_((N)

₁₎

₂

₁ of the imaging parameter for each of the stops W₁

₂

₁-W_((N)

₁₎

₂

₁ of the three-dimensional moving window 102, each of the stops W₁

₂

₁-W_(N)

₂

₁ is in the target space 100, but the stop W_((N)

₁₎

₂

₁ has a left portion within the target space 100 and a right portion inthe outside space 103; the three-dimensional moving window 102 mayrepeat the step (1) row by row in the frontmost two of the MRI slices 10aligned in the z direction for the three-dimensional original map untilthe three-dimensional moving window 102 moves to the bottommost row ofthe three-dimensional original map to repeat in the step (1) in thebottommost row of the three-dimensional original map to obtain one ofthe values C₁

₁

₁--C_((N)

₁₎

_((N)

₁₎

₁ of the imaging parameter for each of the stops W₁

₁

₁-W_((N)

₁₎

_((N)

₁₎

₁ of the three-dimensional moving window 102 as seen in FIG. 31A; eachof the stops W₁

₁

₁-W_(N)

_(N)

₁ is in the target space 100, while each of the stops W_((N)

₁₎

₁

₁-W_((N)

₁₎

_(N)

₁ has a left portion within the target space 100 and a right portion inthe outside space 103, each of the stops W₁

_((N)

₁₎

₁-W_(N)

_((N)

₁₎

₁ has a top portion within the target space 100 and a bottom portion inthe outside space 103, and the stop W_((N)

₁₎

_((N)

₁₎

₁ has a left top portion within the target space 100 and left bottom andright portions in the outside space 103;

(3) moving to the next combination of the MRI slices 10 aligned in the zdirection for the three-dimensional original map with a distance orshift equal to the width Z_(fp) of the cube 106, i.e., computationvoxel, in the z direction to repeat the steps (1) and (2) in a plane ofthe three-dimensional original map to obtain one of the values C_(m)

_(n)

_(u) of the imaging parameter for each of the stops W_(m)

_(n)

_(u) of the three-dimensional moving window 102; the steps (1), (2) and(3) repeat in a space until the three-dimensional moving window 102 moveto the backmost combination of the MRI slices 10 of thethree-dimensional original map to repeat the steps (1) and (2) in thebackmost combination of the MRI slices 10 aligned in the z direction forthe three-dimensional original map; for the example, thethree-dimensional moving window 102 may repeat the steps (1) and (2)plane by plane with a distance or shift equal to the width Z_(fp) of thecube 106 in the z direction from the frontmost two of the MRI slices 10aligned in the z direction for the three-dimensional original map to thebackmost two of the MRI slices 10 aligned in the z direction for thethree-dimensional original map to obtain one of the values C₁

₁

₁-C_((N)

₁₎

_((N)

₁₎

_((N)

₁₎ of the imaging parameter for each of the stops W₁

₁

₁-W_((N)

₁₎

_((N)

₁₎

_((N)

₁₎ of the three-dimensional moving window 102 as seen in FIG. 31B, eachof the stops W₁

₁

₁-W_(N)

_(N)

_(N) is within the target space 100, while each of the stops W_((N)

₁₎

₁

₁-W_((N)

₁₎

_(N)

_(N) has a left portion within the target space 100 and a right portionin the outside space 103, each of the stops W₁

_((N)

₁₎

-W_(N)

_((N)

₁₎

_(N) has a top portion within the target space 100 and a bottom portionin the outside space 103, each of the stops W₁

₁

_((N)

₁₎-W_(N)

_(N)

_((N)

₁₎ has a front portion within the target space 100 and a back portion inthe outside space 103, each of the stops W_((N)

₁₎

_((N)

₁₎

₁-W_((N)

₁₎

_((N)

₁₎

_(N) has a left top portion within the target space 100 and left bottomand right portions in the outside space 103, each of the stops W_((N)

₁₎

₁

_((N)

₁₎-W_((N)

₁₎

_(N)

_((N)

₁₎ has a left front portion within the target space 100 and right frontand back portions in the outside space 103, each of the stops W₁

_((N)

₁₎

_((N)

₁₎-W_(N)

_((N)

₁₎

_((N)

₁₎ has a top front portion within the target space 100 and bottom frontand back portions in the outside space 103, and the stop W_((N)

₁₎

_((N)

₁₎

_((N)

₁₎ has a left-top front portion within the target space 100 andleft-bottom front, right front and back portions in the outside space103.

Referring to FIGS. 27A, 30A and 30B, in the step S27-2, a constant valueof the imaging parameter may be assigned or set for each of the valuesd_((L)

₁

_((H)

₁₎-d_((K)

₁₎

_((L)

₁₎

_((H)

₁₎, d₁

_((L)

₁₎

₁-d_((K)

₁₎

_((L)

₁₎

_((H)

_(1) and d) _((K)

₁₎

₁

₁-d_((K)

₁₎

_((L)

₁₎

_((H)

₁₎ of the imaging parameter for each computation voxel P₁

₁

_((H)

₁₎-P_((K)

₁₎

_((L)

₁₎

_((H)

₁₎, P₁

_((L)

₁₎

₁-P_((K)

₁₎

_((L)

₁₎

_((H)

₁₎ and P_((K)

₁₎

₁

₁-P_((K)

₁₎

_((L)

₁₎

_((H)

₁₎, which in the outside space 103, of the three-dimensionalcomputational map since the outside space 103 is a background outsidethe target space 100, wherein in this case K=L=H=N

1. In the other words, the values d₁

₁

_((H)

₁₎d_((K)

₁₎

_((L)

₁₎

_((H)

₁₎, d₁

_((L)

₁₎

₁-d_((K)

₁₎

_((L)

₁₎

_((H)

₁₎ and d_((K)

₁₎

₁

₁-d_((K)

₁₎

_((L)

₁₎

_((H)

₁₎ of the imaging parameter for the respective computation voxels P₁

₁

_((H)

₁₎-P_((K)

₁₎

_((L)

₁₎

_((H)

₁₎, P₁

_((L)

₁₎

-P_((K)

₁₎

_((L)

₁₎

_((H)

₁₎ and P_((K)

₁₎

₁

₁-P_((K)

₁₎

_((L)

₁₎

_((H)

₁₎ in the outside region 103 become known.

Referring to FIGS. 27A, 30A and 30B, in the step S29-3 for deconvolutionoperation (E_(d)) one of the values d₁

₁

₁-d_(K)

_(L)

_(H) of the imaging parameter for each computation voxel P₁

₁

₁-P_(K)

_(L)

_(H), which is in the target space 100, of the three-dimensionalcomputational map is iteratively updated or calculated, as illustratedin the steps DC1-DC10 in the third aspect, based on one or more of thevalues C₁

₁

₁-C_((N)

₁₎

_((N)

₁₎

_((N)

₁₎ of the imaging parameter for respective one or more of the stops W₁

₁

₁-W_((N)

₁₎

_((N)

₁₎

_((N)

₁₎ each covering said each computation voxel P₁

₁

₁-P_(K)

_(L)

_(H) and/or one or more of the values d_((K)

₁₎

₁

₁-d_((K)

₁₎

_((L)

₁₎

_((H)

₁₎, d₁

_((L)

₁₎

₁-d_((K)

₁₎

_((L)

₁₎

_((H)

₁₎ and d₁

₁

_((H)

₁₎-d_((K)

₁₎

_((L)

₁₎

_((H)

₁₎ of the imaging parameter for respective one or more of thecomputation voxels P_((K)

₁₎

₁

₁-P_((K)

₁₎

_((L)

₁₎

_((H)

₁₎, P₁

_((L)

₁₎

₁-P(_(K)

₁₎

_((L)

₁₎

_((H)

₁₎ and P₁

₁

_((H)

₁₎-P_((K)

₁₎

_((L)

₁₎

_((H)

₁₎ in the outside region 103, each in at least one of the respective oneor more of the stops W₁

₁

₁-W_((N)

₁₎

_((N)

₁₎

_((N)

₁₎. The values d₁

₁

₁-d_(K)

_(L)

_(H) of the imaging parameter for the computation voxels P₁

₁

₁-P_(K)

_(L)

_(H) within the target space 100 are unknown, but the values d_((K)

₁₎

₁

₁-d_((K)

₁₎

_((L)

₁₎

_((H)

₁₎, d₁

_((L)

₁₎

₁-d_((K)

₁₎

_((L)

₁₎

_((H)

₁₎ and d₁

₁

_((H)

₁₎-d_((K)

₁₎

_((L)

₁₎

_((H)

_(1) of the imaging parameter for the computation voxels P) _((K)

₁₎

₁

₁-P_((K)

₁₎

_((L)

₁₎

_((H)

₁₎, P₁

_((L)

₁₎

₁-P_((K)

₁₎

_((L)

₁₎

_((H)

₁₎ and P₁

₁

_((H)

₁₎-P_((K)

₁₎

_((L)

₁₎

_((H)

₁₎, in the outside region 103 become known. Since a ratio of the numberof the known values, including the values C₁

₁

₁-C_((N)

₁₎

_((N)

₁₎

_((N)

₁₎ of the imaging parameter for the stops W₁

₁

₁-W_((N)

₁₎

_((N)

₁₎

_((N)

₁₎ and the values d_((K)

₁₎

₁

₁-d_((K)

₁₎

_((L)

₁₎

_((H)

₁₎, d₁

_((L)

₁₎

₁-_((K)

₁₎

_((L)

₁₎

_((H)

₁₎, and d₁

₁

_((H)

₁₎-d_((K)

₁₎

_((L)

₁₎

_((H)

₁₎ of the imaging parameter for the computation voxels P(_(K)

₁₎

₁

₁-P_((K)

₁₎

_((H)

₁₎

_((L)

₁₎, P₁

_((L)

₁₎

₁-P_((K)

₁₎

_((L)

₁₎

_((H)

₁₎ and P₁

₁

_((H)

₁₎-P_((K)

₁₎

_((L)

₁₎

_((H)

₁₎ in the outside space 103, to the number of the unknown values d₁

₁

₁-d_(K)

_(L)

_(H) of the imaging parameter for the computation voxels P₁

₁

₁-P_(K)

_(L)

_(H) increases, each of the unknown values d₁

₁

₁-d_(K)

_(L)

_(H) of the imaging parameter for the computation voxels P₁

₁

₁-P_(K)

_(L)

_(H) in the target space 100 may be shortly updated into an optimalvalue of the imaging parameter by computer iterative computation asmentioned in the third aspect. For example, the value d_(K)

_(L)

_(H) of the imaging parameter for the computation voxel P_(K)

_(L)

_(H), which is in the target space 100, of the three-dimensionalcomputational map is iteratively updated or calculated, as illustratedin the steps DC1-DC10 in the third aspect, based on the values C_(N)

_(N)

_(N)-C_((N)

₁₎

_((N)

₁₎

_((N)

₁₎ of the imaging parameter for the respective stops W_(N)

_(N)

_(N)-W_((N)

₁₎

_((N)

₁₎

_((N)

₁₎ each covering the computation voxel P_(K)

_(L)

_(H) and the values d_((K)

₁₎

_((L)

₁₎

_((H)

₁₎-d_((K)

₁₎

_((L)

₁₎

_((H)

₁₎, d_((K)

₁₎

_((L)

₁₎

_((H)

₁₎-d_((k)

₁₎

_((L)

₁₎

_((H)

₁₎ and d_((K)

₁₎

_((L)

₁₎

_((H)

₁₎-d_((K)

₁₎

_((L)

₁₎

_((H)

₁₎ of the imaging parameter for the respective computation voxels P_((K)

₁₎

_((L)

₁₎

_((H)

₁₎-P_((K)

₁₎

_((L)

₁₎

_((H)

₁₎, P_((K)

₁₎

_((L)

₁₎

_((H)

₁₎-P_((K)

₁₎

_((L)

₁₎

_((H)

₁₎ and P_((K)

₁₎

_((L)

₁₎

_((H)

₁₎-P_((K)

₁₎

_((L)

₁₎

_((H)

_(1) in the outside region 103, each in at least one of the stops W)_(N)

_(N)

_(N)-W_((N)

₁₎

_((N)

₁₎

_((N)

₁₎.

Alternatively, one of the values d₁

₁

₁-d_(K)

_(L)

_(H) of the imaging parameter for each of the computation voxels P₁

₁

₁-P_(K)

_(L)

_(H) within the target space 100 may be solved from the value d_(K)

_(L)

_(H) of the imaging parameter for the computation voxel P_(K)

_(L)

_(H) at a corner of the target space 100 among the right-side,bottom-side and backside borders of the target space 100, as describedin the following method. At the beginning, the value d_(K)

_(L)

_(H) of the imaging parameter for the computation voxel P_(K)

_(L)

_(H) at the corner of the target space 100 among the right-side,bottom-side and backside borders of the target space 100 may be firstcalculated. Next, the values d₁

₁

₁-d_((K)

₁₎

_(L)

_(H), d_(K)

₁

₁-d_(K)

_((L)

₁₎

_(H) and d_(K)

_(L)

₁-d_(K)

_(L)

_((H)

₁₎ of the imaging parameter for the respective computation voxels P₁

₁

₁-P_((K)

₁₎

_(L)

_(H), P_(K)

_(L)

₁-P_(K)

_((L)

₁₎

_(H) and P_(K)

_(L)

₁-P_(K)

_(L)

_((H)

₁₎ within the target space 100 may be solved voxel by voxel one of thevalues d_(k)

_(l)

_(h) of the imaging parameter for one of the computation voxels P_(k)

_(l)

_(h) to another value d_((k)

₁₎

_(l)

_(h) of the imaging parameter for another computation voxel P_((k)

₁₎

_(l)

_(h) shifted from said one of the computation voxels P_(k)

_(l)

_(h) by the width X_(fp) of the computation voxels P_(k)

_(l)

_(h) in the leftward direction, from one of the values d_(k)

_(l)

_(h) of the imaging parameter for one of the computation voxels P_(k)

_(l)

_(h) to another value d_(k)

_((l)

₁₎

_(h) of the imaging parameter for another computation voxel P_(k)

_((l)

₁₎

_(h) shifted from said one of the computation voxels P_(k)

_(l)

_(h) by the width Y_(fp) of the computation voxels P_(k)

_(l)

_(h) in the upward direction, or from one of the values d_(k)

_(l)

_(h) of the imaging parameter for one of the computation voxels P_(k)

_(l)

_(h) to another value d_(k)

_(l)

_((h)

₁₎ of the imaging parameter for another computation voxel P_(k)

_(l(h)

₁₎ shifted from said one of the computation voxels P_(k)

_(l)

_(h) by the width Z_(fp) of the computation voxels P_(k)

_(l)

_(h) in the frontward direction.

V-4. Computational Map Derived from Measured Values for Stops ofThree-dimensional Moving Window

Alternatively, the process as illustrated in FIG. 27B is the same asthat as illustrated in FIG. 27A except that the step S27-1 is replacedwith a step S27-4. Referring to FIGS. 27B, 30A and 30B, in the stepS27-4, a three-dimensional moving window 102 may be applied to athree-dimensional space divided into a target space 100 and an outsidespace 103 around the target space 10 to measure a value C₁

₁

₁-C_((N)

₁₎

_((N)

₁₎

_((N)

₁₎ of an imaging parameter, such as parameter of T1, T2, Ktrans or taufor an MRI parameter or parameter obtained from a wave penetratingdevice, for each stop W₁

₁

₁-W_((N)

₁₎

_((N)

₁₎

_((N)

₁₎ of the three-dimensional moving window 102, wherein some stops W_((N)

₁₎

₁

₁-W_((N)

₁₎

_((N)

₁₎

_((N)

₁₎, W₁

_((N)

₁₎

_(L)-W_((N)

₁₎

_((N)

₁₎

_((N)

₁₎ and W_(L)

₁

_((N)

₁₎-W_((N)

₁₎

_((N)

₁₎

_((N)

₁₎ of the three-dimensional moving window 102 partially overlap thetarget and outside spaces 100 and 103. The step S27-4 for moving thethree-dimensional moving window 102 in the path across thethree-dimensional space may be referred to the step S27-1 for the same.Each neighboring two of the stops W₁

₁

₁-W_((N)

₁₎

_((N)

₁₎

_((N)

₁₎ in the x direction may partially overlap with each other with a shiftequal to the x-direction width X_(fp) of the computation voxels P₁

₁

₁-P_((K)

₁₎

_((L)

₁₎

_((H)

₁₎ of the three-dimensional computational map. Each neighboring two ofthe stops W₁

₁

₁-W_((N)

₁₎

_((N)

₁₎

_((N)

₁₎ in the y direction may partially overlap with each other with a shiftequal to the y-direction width Y_(fp) of the computation voxels P₁

₁

₁-P_((K)

₁₎

_((L)

₁₎

_((H)

₁₎ of the three-dimensional computational map. Each neighboring two ofthe stops W₁

₁

₁-W_((N)

₁₎

_((N)

₁₎

_((N)

₁₎ in the z direction may partially overlap with each other with a shiftequal to the z-direction width Z_(fp) of the computation voxels P₁

₁

₁-P_((K)

₁₎

_((L)

₁₎

_((H)

₁₎ of the three-dimensional computational map.

One or more of computed tomography (CT) parameters, positron emissiontomography (PET) parameters, single-photon emission computed tomography(SPECT) parameters, micro-PET parameters, micro-SPECT parameters, Ramanparameters, and/or bioluminescence optical (BLO) parameters, ultrasoundparameters, camera-image parameters and/or visible-light-imageparameters may be measured for the value C₁

₁

₁-C_((N)

₁₎

_((N)

₁₎

_((N)

₁₎ of the imaging parameter for said each stop W₁

₁

-W_((N)

₁₎

_((N)

₁₎

_((N)

₁₎ of the three- dimensional moving window. The value C₁

₁

₁-C_((N)

₁₎

_((N)

₁₎

_((N)

₁₎ of the imaging parameter for said each stop W₁

₁

₁-W_((N)

₁₎

_((N)

₁₎

_((N)

₁₎ of the three-dimensional moving window may be measured from detectionor analysis instruments, such as camera, microscope (optical orelectronic), endoscope, detectors or spectrometer (visible light,fluorescent light, IR, UV or X-ray), ultrasonic machine or system,magnetic resonance imaging (MRI) machine or system, computed tomography(CT) machine or system, positron emission tomography (PET) machine orsystem, single-photon emission computed tomography (SPECT) machine orsystem, micro-PET machine or system, micro-SPECT machine or system,Raman spectrometer or system, and/or bioluminescence optical (BLO)machine or system, or other machine for obtaining molecular orstructural imaging data.

Next, referring to FIG. 27B, the steps S27-2 and S27-3 as illustrated inFIGS. 27A, 30A and 30B continues.

V-5. Probability Map Derived from Measured Values for Original Pixels ofTwo-Dimensional Original Map

FIG. 28A illustrates a process of using an E operator to obtain betterresolution or probabilities of an event in a two-dimensional region orthree-dimensional space in accordance with an embodiment of the presentapplication. Referring to FIGS. 28A and 29A-29D, in a step S28-1 forconvolution operation (E_(c)), a two-dimensional moving window 2 may beapplied to one or a plurality of two-dimensional original mapsregistered to or aligned with each other or one another, wherein the oneor each of the plurality of two-dimensional original maps is providedwith multiple original measured values of a specific one of one or moreimaging parameters, such as parameter of T1, T2, Ktrans or tau for anMRI parameter or parameter obtained from an optical image captured by acamera, each for one of its original pixels p_(i)

_(j) arranged in a two-dimensional array, wherein the one or each of theplurality of two-dimensional original maps is registered to andassociated with and covers a two-dimensional region divided into atarget region 11 for a biological structure and an outside region 103for a reference or predetermined structure such as glass or metal aroundthe target region 11, to obtain one or a set of values C₁

₁-C_((M)

₂₎

_((N)

₂₎ of the one or more imaging parameters, such as parameters of T1, T2and Ktrans for MRI parameters, parameters of T1, T2 and tau for MRIparameters or parameters obtained from one or more optical imagescaptured by one or more cameras, for each stop W₁

₁-W_((M)

₂₎

_((N)

₂₎ of the two-dimensional moving window 2, wherein some stops W_((M)

₁₎

₁-W_((M)

₂₎

_((N)

₂₎ and W_(L)

_((N)

₁₎-W_(M)

_((N)

₂₎ of the two-dimensional moving window 2 partially overlap the targetand outside regions 11 and 103. In this case, the original measuredvalues for the respective original pixels p_(i)

_(j) of the one or each of the plurality of two-dimensional originalmaps may be associated with an MRI parameter; the one or each of theplurality of two-dimensional original maps may be associated with an MRIslice registered to or aligned with the two-dimensional region. The oneor each of the set of values C₁

₁-C_((M)

₂₎

_((N)

₂₎ of a specific one of the one or more imaging parameters for said eachstop W₁

₁-W_((M)

₂₎

_((N)

₂₎ of the two-dimensional moving window 2 is calculated or obtainedbased on one or more of the original measured values of the specific oneof the one or more imaging parameters for respective one or more of theoriginal pixels p_(i)

_(j) of the one or one of the plurality of two-dimensional originalmaps, which are covered by or associated with said each stop W₁

₁-W_((M)

₂₎

_((N)

₂₎ of the two-dimensional moving window 2. Said each stop W₁

₁-W_((M)

₂₎

_((N)

₂₎ of the two-dimensional moving window 2 has a larger area than that ofeach of the respective one or more of the original pixels p_(i)

_(j) of the one or each of the plurality of two-dimensional originalmaps. Each neighboring two of the stops W₁

₁-W_((M)

₂₎

_((N)

₂₎ in a x direction may partially overlap with each other with a shiftequal to a x-direction width X_(fp) of computation pixels P₁

₁-P_((K)

_(2)=(L)

₂₎ of a two-dimensional computational map 12. Each neighboring two ofthe stops W₁

₁-W_((M)

₂₎

_((N)

₂₎ in a y direction may partially overlap with each other with a shiftequal to a y-direction width Y_(fp) of the computation pixels P₁

₁-P_((K)

₂₎

_((L)

₂₎ of the two-dimensional computational map 12.

Next, referring to FIGS. 28A and 29A-29D, in a step S28-2 for big-dataengineering learning, a probability CL₁

₁-CL_((M)

₂₎

_((N)

₂₎ of an event for each stop W₁

₁-W_((M)

₂₎

_((N)

₂₎ of the two-dimensional moving window 2 may be calculated or obtainedby matching the one or the set of values C₁

₁C_((M)

₂₎

_((N)

₂₎ of the one or more imaging parameters for said each stop W₁

₁-W_(M)

₂₎

_((N)

₂₎ of the two-dimensional moving window 2 to a classifier such asBayesian classifier as illustrated in the first aspect.

Referring to FIGS. 28A and 29A-29D, in a step S31-3, a constantprobability of the event may be assigned or set for each of theprobabilities and of the event for each computation pixel P_((K)

₁₎

_(L)-P_((K)

₂₎

_((L)

₂₎ and P₁

_((L)

₁₎-P_(K)

_((L)

₂₎ of the event, which is in the outside region 103, of thetwo-dimensional computational map 12 since the outside region 103 is abackground outside the target region 11. In the other words, theprobabilities dl_((K)

₁₎

_(L)-dl_((K)

₂₎

_((L)

₂₎ and dl₁

_((L)

₁₎-dl_(K)

_((L)

₂₎ of the event for the respective computation pixels P_((K)

₁₎

_(L)-P_((K)

₂₎

_((L)

₂₎ and P₁

_((L)

₁₎-P_(K)

_((L)

₂₎ in the outside region 103 become known.

Next, referring to FIGS. 28A and 29A-29D, in a step S31-4 fordeconvolution operation (E_(d)), one of the probabilities dl₁

₁-dl_(K)

_(L) of the event for each computation pixel P_(L)

₁-P_(K)

_(L), which is in the target region 11, of the two-dimensionalcomputational map 12 is iteratively updated or calculated, asillustrated in the steps ST1-ST11 in the first aspect, based on one ormore of the probabilities CL₁

₁-CL_((M)

₂₎

_((N)

₂₎ of the event for respective one or more of the stops W₁₋₁-W_((M)

₂₎

_((N)

₂₎ each covering said each computation pixel P₁

₁-P_(K)

_(L and/or one or more of the probabilities dl) _((K)

_(L))

₁-dl_((K)

₂₎

_((L)

₂₎ and dl₁

_((L)

₁₎-dl_(K)

_((L)

₂₎ of the event for respective one or more of the computation pixels P(K

1)

1-P_((K)

₂₎

_((L)

₂₎ and P₁

_((L)

₁₎-P_(K)

_((L)

₂₎ in the outside region 103, each in at least one of the respective oneor more of the stops W₁

₁-W_((M)

₂₎

_((N)

₂₎. Said each computation pixel P₁

₁-P_(K)

_(L) has a smaller area than that of each of the respective one or moreof the stops W₁

₁-W_((M)

₂₎

_((N)

₂₎ of the two-dimensional moving window 2. The probabilities dl₁

₁-dl_(K)

_(L) of the event for the respective computation pixels P₁₋₁-P_(K)

_(L) within the target region 11 are unknown, but the probabilitiesdl_((K)

_(L))

₁-dl_((K)

₂₎

_((L)

₂₎ and dl₁

_((L)

₁₎-dl_(K)

_((L)

₂₎ of the event for the respective imputation pixels P_((K)

_(L))

₁-P_((K)

₂₎

_((L)

₂₎ and P₁

_((L)

₁₎-P_((K)

₂₎

_((L)

₂₎ in the outside region 103 become known. Since the ratio of the numberof the known probabilities of the event, including the probabilities CL₁

₁-CL_((M)

₂)

(N

2) of the event for the stops W₁

₁W_((M)

₂₎

_((N)

₂₎ and the probabilities dl_((K)

₁₎

_(L)-dl_((K)

₂₎

_((L)

₂₎ and dl₁

_((L)

₁₎-dl_(K)

_((L)

₂₎ of the event for the respective computation pixels P_((K)

₁₎

₁-P_((K)

₂₎

_((L)

₂₎ and P₁

_((L)

₁₎-P_(K)

_((L)

₂₎ in the outside region 103, to the number of the unknown probabilitiesdl₁

₁-dl_(K)

_(L) of the event for the respective computation pixels P₁

₁-P_(K)

_(L) increases, each of the unknown probabilities dl₁

₁-dl_(K)

_(L) of the event for the respective computation pixels P₁

₁-P_(K)

_(L) in the target region 11 may be shortly updated into an optimalprobability of the event by computer iterative computation as mentionedin the first aspect. For example. the probability dl_(K)

_(L) of the event for the computation pixel P_(K)

_(L), which is in the target region 11, of the two-dimensionalcomputational map is iteratively updated or calculated, as illustratedin the steps ST1-ST11 in the first aspect, based on the probabilitiesCL_(M)

_(N)-CL_((M)

₂₎

_((N)

₂₎ of the event for the respective stops W_(M)

_(N)-W_((M)

₂₎

_((N)

₂₎ each covering the computation pixel P_(K)

_(L) and the probabilities dl_((K)

₁₎

_((L)

₂₎, dl_((K)

₂₎

_((L)

₂₎, dl_((K)

₁₎

_((L)

₁₎, dl_((K)

₂₎

_((L)

_(1), dl) _((K)

₁₎

_(L), dl_((K)

₂₎

_(L), dl_((K)

₂₎

_((L)

₁₎, dl_((K)

₁₎

_((L)

₁₎, dl_(K)

_((L)

₁₎, dl_((K)

₁₎

_((L)

₁₎, dl_((K)

₂₎

_((L)

₁), dl_((K)

₂₎

_((L)

₂₎, dl_((K)

₁₎

_((L)

₂₎, dl_(K)

_((L)

₂₎, dl(K

1)

(L

2) and dl_((K)

₂₎

_((L)

₂₎ of the event for the respective computation pixels P_((K)

₁₎

_((L)

₂₎, P_((K)

₂₎

_((L)

₂₎, P_((K)

₂₎

_((L)

₁₎, P_((K)

₂₎

_((L)

₁₎, P_((K)

₁₎

_(L), P_((K)

₂₎

_(L), P_((K)

₂₎

_((L)

₁₎, P_((K)

₁₎

_((L)

₁₎, P_(K)

_((L)

₁₎, P_((K)

₁₎

_((L)

₁₎, P_((K)

₂₎

_((L)

₁₎, P_((K)

₂₎

_((L)

₂₎, P_((K)

₁₎

_((L)

₂₎, P_(K)

_((L)

₂₎, P_((K)

₁₎

_((L)

₂₎ and P_((K)

₂₎

_((L)

₂₎ in the outside region 103. each in at least one of the stops W_(M)

_(N)-W_((M)

₂₎

_((N)

₂₎.

Alternatively, referring to FIGS. 28A and 29A-29D, one of theprobabilities dl₁

₁-dl_(K)

_(L) of the event for each of the computation pixels P₁

₁-P_(K)

_(L) within the target region 11 may be solved from the probabilitydl_(K)

_(L) of the event for the computation pixel P_(K)

_(L) at a corner of the target region 11 between the right-side andbottom-side borders of the target region 11, as described in thefollowing method. At the beginning, the probability dl_(K)

_(L) of the event for the computation pixel P_(K)

_(L) at the corner of the target region 11 between the right-side andbottom-side borders of the target region 11 may be first calculated.Next, the probabilities dl₁

₁-dl_((K)

₁₎

_((L)

₁₎, dl_(K)

_(L)-dl_(K)

_((L)

₁₎ and dl₁

_(L)-dl_((K)

₁₎

_(L) of the event for the respective computation pixels P₁

₁-P_((K)

₁₎

_((L)

₁₎, P_(K)

₁-P_(K)

_((L)

₁₎ and P₁

_(L)-P_((K)

₁₎

_(L) in the target region 11 may be solved pixel by pixel from one ofthe probability dl_(k)

_(l) of the event for one of the computation pixels P_(k)

₁ to another probability dl_((k)

₁₎

_(l) of the event for another computation pixel P_((k)

₁₎

_(l) shifted from said one of the computation pixels P_(k)

_(l) in the leftward direction; the probabilities dl₁

₁-dl_((K)

₁₎

_((L)

₁₎, dl_(k)

₁-dl_(K)

_((L)

₁₎ and dl₁

_(L)-dl_((K)

₁₎

_(L) of the event for the respective computation pixels P₁

₁-P_((K)

₁₎

_((L)

_(1), P) _(K)

_(L)-P_(K)

_((L)

₁₎ and P₁

₁-P_((K)

₁₎

_(L) in the target region 11 may be solved pixel by pixel from one ofthe probabilities dl_(k)

_(l) of the event for one of the computation pixels P_(k)

_(l) to another probability dl_(k)

_((l)

₁₎ of the event for another computation pixel P_(k)

_((l)

₁₎ shifted from said one of the computation pixels P_(k)

_(l) the upward direction. The calculation for the probabilities dl₁

₁-dl_(K)

_(L) of the event herein may be referred to the calculation for thevalues d₁

₁-d_(K)

_(L) of the imaging parameter solved from the value d_(K)

_(L) of the imaging parameter as above mentioned in FIG. 27A and 29A-29Din the section of V-1.

V-6. Probability Map Derived from Measured Values for Stops ofTwo-Dimensional Moving Window

Alternatively, FIG. 28B illustrates another process of using an Eoperator to obtain better resolution of probabilities of an event in atwo-dimensional region in accordance with an embodiment of the presentapplication. Referring to FIGS. 28B and 29A-29D, in a step S28-5, atwo-dimensional moving window 2 may be applied to a two-dimensionalregion divided into a target region 11 for a biological structure and anoutside region 103 for a reference or predetermined structure such asglass or metal around the target region 11 by moving step by step on thetwo-dimensional region with a shift equal to a x-direction width X_(fp)of computation pixels P₁

₁-P_((K)

₂₎

_((L)

₂₎ of a two-dimensional computational map 12 and moving row by row onthe two-dimensional region with a shift equal to a y-direction widthY_(fp) of the computation pixels P₁

₁-P_((K)

₂₎

_((L)

₂₎ of the two-dimensional computational map 12 to measure one or a setof values C₁

₁-C_((M)

₂₎

_((N)

₂₎ of one or more imaging parameters, such as parameters of T1, T2 andKtrans for MRI parameters, parameters of T1, T2 and tau for MRIparameters or parameters obtained from one or more optical imagescaptured by one or more cameras, for each stop W₁

₁-W_((M)

₂₎

_((N)

₂₎ of the two-dimensional moving window 2. Each neighboring two of thestops W₁

₁-W_((M)

₂₎

_((N)

₂₎ in a x direction may partially overlap with each other with a shiftequal to a x-direction width X_(fp) of the computation pixels P₁

₁-P_((K)

₂₎

_((L)

₂₎ of the two-dimensional computational map 12. Each neighboring two ofthe stops W₁

₁-W_((M)

₂₎

_((N)

₂₎ in a y direction may partially overlap with each other with a shiftequal to a y-direction width Y_(fp) of the computation pixels P₁

₁--P_((K)

₂₎

_((L)

₂₎ of the two-dimensional computational map 12.

One or more of computed tomography (CT) parameters, positron emissiontomography (PET) parameters, single-photon emission computed tomography(SPECT) parameters, micro-PET parameters, micro-SPECT parameters, Ramanparameters, and/or bioluminescence optical (BLO) parameters, ultrasoundparameters, camera-image parameters and/or visible-light-imageparameters may be measured for the one or the set of values C₁

₁-C_((M)

₂₎

_((N)

₂₎ for said each stop W₁

₁-W_((M)

₂₎

_((N)

₂₎ of the two-dimensional moving window. The one or the set of values C₁

₁-C_((M)

₂₎

_((N)

₂₎ of the one or more imaging parameters for said each stop W₁

₁-W_((M)

₂₎

_((N)

₂₎ of the two-dimensional moving window may be measured from detectionor analysis instruments, such as camera, microscope (optical orelectronic), endoscope, detectors or spectrometer (visible light,fluorescent light, IR, UV or X-ray), ultrasonic machine or system,magnetic resonance imaging (MRI) machine or system, computed tomography(CT) machine or system, positron emission tomography (PET) machine orsystem, single-photon emission computed tomography (SPECT) machine orsystem, micro-PET machine or system, micro-SPECT machine or system,Raman spectrometer or system, and/or bioluminescence optical (BLO)machine or system, or other machine for obtaining molecular orstructural imaging data.

Next, referring to FIG. 28B, the steps S28-2 through S28-4 asillustrated in FIGS. 28A and 29A-29D for the fifth aspect continue.Thereby, the algorithm may be employed to transform the one or the setof values C₁

₁-C_((M)

₂₎

_((N)

₂₎ of the one or more imaging parameters for said each stop W₁

₁-W_((M)

₂₎

_((N)

₂₎ of the two-dimensional moving window into the probability dl₁

₁-dl_(K)

_(L) of the event for said each computation pixel P₁

₁-P_(K)

_(L) of the two-dimensional computational map having better resolution.

V-7. Probability Map Derived from Measured Values for Original Voxels ofThree-Dimensional Original Map

Alternatively, referring to FIGS. 28A and 30A and 30B, in the step S28-1for convolution operation (E_(c)), the 3D moving window 102 as seen inFIG. 25 may be applied to one or a plurality of three-dimensionaloriginal maps registered to or aligned with each other or one another,wherein the one or each of the plurality of three-dimensional originalmaps is provided with multiple original measured values of a specificone of one or more imaging parameters, such as parameter of T1, T2,Ktrans or tau for an MRI parameter or parameter obtained from a wavepenetrating device configured to generate a wave to penetrate a targetspace 100, each for one of its original voxels p_(i)

_(j)

_(g) arranged in a three-dimensional array, wherein the one or each ofthe plurality of the three-dimensional original maps is registered toand associated with and covers the target space 100 for a biologicalstructure and an outside space 103 for a reference or predeterminedstructure such as glass or metal around the target space 100, to obtainone or a so of values C₁

₁

₁-C_((N)

₁₎

_((N)

₁₎

_((N)

₁₎ of the one or more imaging parameters, such as parameters of T1, T2and Ktrans for MRI parameters, parameters of T1, T2 and tau for MRIparameters or parameters obtained from the wave penetrating device, foreach stop W₁

₁

₁-W_((N)

₁₎

_((N)

₁₎

_((N)

₁₎ of the three-dimensional moving window 102, wherein some stops W₁

₁

_((N)

₁₎-W(_(N)

₁₎

_((N)

₁₎

_((N)

₁₎, W₁

_((N)

₁₎

₁-W(N

1)

(N

1)

(N

1) and W_((N)

₁₎

₁

₁-W_((N)

₁₎

_((N)

₁₎

_((N)

₁₎ of the three-dimensional moving window 102 partially overlap thetarget and outside spaces 100 and 103. In this case, the originalmeasured values for the respective original voxels p_(i)

_(j)

_(g) of the one or each of the plurality of three-dimensional originalmaps may be associated with an MRI parameter, the one or each of theplurality of three-dimensional original maps may be associated with anMRI slice or a combination of multiple MRI slices registered to oraligned with a combination of the target and outside spaces 100 and 103.The one or each of the set of values C₁

₁

₁-C_((N)

₁₎

_((N)

₁₎

_((N)

₁₎ of a specific one of the one or more imaging parameters for said eachstop W₁

₁

₁-W_((N)

₁₎

_((N)

₁₎

_((N)

₁₎ of the three-dimensional moving window 102 is calculated or obtainedbased on one or more of the original measured values of the specific oneof the one or more imaging parameters for respective one or more of theoriginal voxels p_(i)

_(j)

_(g) of the one or one of the plurality of three-dimensional originalmaps, which are covered by or associated with said each stop W₁

₁

₁-W_((N)

₁₎

_((N)

₁₎

_((N)

₁₎ of the three-dimensional moving window 102. Said each stop W₁

₁

₁-W_((N)

₁₎

_((N)

₁₎

_((N)

₁₎ of the three-dimensional moving window 102 has a larger volume thanthat of each of the respective one or more of the original voxels p_(i)

_(j)

_(g) of the one or each of the plurality of three-dimensional originalmaps. Each neighboring two of the stops W₁

₁

₁-W_((N)

₁₎

_((N)

₁₎

_((N)

₁₎ in a x direction may partially overlap with each other with a shiftequal to a x-direction width X_(fp) of computation voxels P₁

₁

₁-P(K

1)

(L

1)

(H

1) of a three-dimensional computational map. Each neighboring two of thestops W₁

₁

₁-W_((N)

₁₎

_((N)

₁₎

_((N)

₁₎ in a y direction may partially overlap with each other with a shiftequal to a y-direction width Y_(fp) of the computation voxels P₁

₁

₁-P_((K)

₁₎

_((L)

₁₎

_((H)

₁₎ of the three-dimensional computational map. Each neighboring two ofthe stops W₁

₁

₁-W_((N)

₁₎

_((N)

₁₎

_((N)

₁₎ in a z direction may partially overlap with each other with a shiftequal to a z-direction width Z_(fp) of the computation voxels P₁

₁

₁-P_((K)

₁₎

_((L)

₁₎

_((H)

₁₎ of the three-dimensional computational map. The step S28-1 for movingthe three-dimensional moving window 102 in the path across thecombination of the target and outside spaces 100 and 103 may be referredto the step S27-1 as illustrated in FIGS. 27A, 30A and 30B for movingthe three-dimensional moving window 102 in the path across thecombination of the target and outside spaces 100 and 103.

Next, referring to FIG. 28A, in the step S28-2 for big-data engineeringlearning, a probability CL₁

₁

₁-CL_((N)

₁₎

_((N)

₁₎

_((N)

₁₎ of an event for each stop W₁

₁

₁-W_((N)

₁₎

_((N)

₁₎

_((N)

₁₎ of the three-dimensional moving window 102 may be calculated bymatching the one of the set of values C₁

₁

₁-C_((N)

₁₎

_((N)

₁₎

_((N)

₁₎ of the one or more imaging parameters for said each stop W₁

₁

₁-W_((N)

₁₎

_((N)

₁₎

_((N)

₁₎ of the three-dimensional moving window 102 to a classifier such asBayesian classifier.

Next, referring to FIG. 28A, in the step S28-3, a constant probabilityof the event may be assigned or set for each of the probabilities dl₁

₁

_((H)

₁₎-dl_((K)

₁₎

_((L)

₁₎

_((H)

₁₎, dl₁

_((L)

₁₎

₁-dl_((K)

₁₎

_((L)

₁₎

_((H)

₁₎ and dl_((K)

₁₎

₁

₁-dl_((K)

₁₎

_((L)

₁₎

_((H)

₁₎ of the event for each computation voxel P₁

₁

_((H)

₁₎-P_((K)

₁₎

_((L)

₁₎

_((H)

₁₎, P₁

_((L)

₁₎

₁-P_((K)

₁₎

_((L)

₁₎

_((H)

₁₎ and P_((K)

₁₎

₁

₁-P_((K)

₁₎

_((L)

₁₎

_((H)

₁₎, which is in the outside space 103, of a three-dimensionalcomputational map since the outside space 103 is a background outsidethe target space 100. In this case, K=L=H=N

1. In the other words, the probabilities dl₁

₁

_((H)

₁₎-dl_((K)

₁₎

_((L)

₁₎

_((H)

₁₎, dl₁

_((L)

₁₎

₁-dl_((K)

₁₎

_((L)

₁₎

_((H)

₁₎ and dl_((K)

₁₎

₁

₁-dl_((K)

₁₎

_((L)

₁₎

_((H)

₁₎ of the event for the respective computation voxels P₁

₁

_((H)

₁₎-P_((K)

₁₎

_((L)

₁₎

_((H)

₁₎, P₁

_((L)

₁₎

₁-P_((K)

₁₎

_((L)

₁₎

_((H)

₁₎ and P_((K)

₁₎

₁

₁-P_((K)

₁₎

_((L)

₁₎

_((H)

₁₎ in the outside region 103 become known.

Referring to FIGS. 28A, 30A and 30B, in the step S28-4 for deconvolutionoperation (E_(d)), one of the probabilities dl₁

₁

₁-dl_(K)

_(L)

_(H) of the event for each computation voxel P₁

₁

₁-P_(K)

_(L)

_(H), which is in the target space 100, of the three-dimensionalcomputational map is iteratively updated or calculated, as illustratedin the steps DL1-DL10 in the fourth aspect, based on one or more of theprobabilities CL₁

₁

₁-CL_((N)

₁₎

_((N)

₁₎

_((N)

₁₎ of the event for respective one or more of the stops W₁

₁

₁-W_((N)

₁₎

_((N)

₁₎

_((N)

₁₎ each covering said each computation voxel P₁

₁

₁-P_(K)

_(L)

_(H) and/or one or more of the probabilities dl_((K)

₁₎

₁

₁-dl_((K)

₁₎

_((L)

₁₎

_((H)

₁₎, dl₁

_((L)

₁₎

₁-dl_((K)

₁₎

_((L)

₁₎

_((H)

₁₎and dl₁

₁

_((H)

₁₎-dl_((K)

₁₎

_((L)

₁₎

_((H)

₁₎ of the event for respective one or more of the computation voxelsP_((K)

₁₎

₁

₁-P_((K)

₁₎

_((L)

₁₎

_((H)

₁₎, P₁

_((L)

₁₎

₁-P_((K)

₁₎

_((L)

₁₎

_((H)

₁₎ and P₁

₁

_((H)

₁₎-P_((K)

₁₎

_((L)

₁₎

_((H)

₁₎ in the outside region 103, each in at least one of the respective oneor more of the stops W₁

₁

₁-W_((N)

₁₎

_((N)

₁₎

_((N)

₁₎. The probabilities dl₁

₁

₁-dl_(K)

_(L)

_(H) of the event for the computation voxels P₁

₁

₁-P_(K)

_(L)

_(H) within the target space 100 are unknown, but the probabilitiesdl_((K)

₁₎

₁

₁-dl_((K)

₁₎

_((L)

₁₎

_((H)

₁₎, dl₁

_((L)

₁₎

₁-dl_((K)

₁₎

_((L)

₁₎

_((H)

₁₎ and dl₁

₁

_((H)

₁₎-dl_((K)

₁₎

_((L)

₁₎

_((H)

₁₎of the event for the computation voxels P_((K)

₁₎

₁

₁-P_((K)

₁₎

_((L)

₁₎

_((H)

₁₎, P₁

_((L)

₁₎

₁-P_((K)

₁₎

_((L)

₁₎

_((H)

₁₎ and P₁

₁

_((H)

₁₎-P_((K)

₁₎

_((L)

₁₎

_((H)

₁₎ in the outside region 103 become known. Since the ratio of the numberof the known values, including the probabilities CL₁

₁

₁-CL_((N)

₁₎

_((N)

₁₎

_((N)

₁₎ of the event for the stops W₁

₁

₁-W_((N)

₁₎

_((N)

₁₎

_((N)

₁₎ and the probabilities dl_((K)

₁₎

₁

₁-dl_((K)

₁₎

_((L)

₁₎

_((H)

₁₎ , dl₁

_((L)

₁₎

₁-dl_((K)

₁₎

_((L)

₁₎

_((H)

₁₎ and dl₁

₁

_((H)

₁₎-dl_((K)

₁₎

_((L)

₁₎

_((H)

₁₎ of the event for the computational voxels P_((K)

₁₎

₁

₁-P_((K)

₁₎

_((L)

₁₎

_((H)

₁₎, P₁

_((L)

₁₎

₁-P_((K)

₁₎

_((L)

₁₎

_((H)

₁₎ and P₁

₁

_((H)

₁₎-P_((K)

₁₎

_((L)

₁₎

_((H)

₁₎ in the outside space 103, to the number of the unknown probabilitiesdl₁

₁

₁-dl_(K)

_(L)

_(H) of the event for the computation voxels P₁

₁

₁-P_(K)

_(L)

_(H) increasers, each of the unknown probabilities dl₁

₁

₁-dl_(K)

_(L)

_(H) of the event for the computation voxels P₁

₁

₁-P_(K)

_(L)

_(H) in the target space 100 may be shortly updated into an optimalprobability the event by computer iterative computation as mentioned inthe fourth aspect. For example, the probability dl_(K)

_(L)

_(H) of the event for the computation voxel P_(K)

_(L)

_(H), which is in the target space 100, of the three-dimensionalcomputational map is iteratively updated or calculated, as illustratedin the steps DL1-DL10 in the fourth aspect, based on the probabilitiesCL_(N)

_(N)

_(N)-CL_((N)

₁₎

_((N)

₁₎

_((N)

₁₎ of the event for the respective stops W_(N)

_(N)

_(N)-W_((N)

₁₎

_((N)

₁₎

_((N)

₁₎ each covering the computation voxel P_(K)

_(L)

_(H) and the probabilities dl_((K)

₁₎

_((L)

₁₎

_((H)

₁₎-dl_((K)

₁₎

_((L)

₁₎

_((H)

₁₎, dl_((K)

₁₎

_((L)

₁₎

_((H)

₁₎- dl_((K)

₁₎

_((L)

₁₎

_((H)

₁₎ and dl_((K)

₁₎

_((L)

₁₎

_((H)

₁₎-dl_((K)

₁₎

_((L)

₁₎

_((H)

₁₎ of the event for the respective computation voxels P_((K)

₁₎

_((L)

₁₎

_((H)

₁₎-P_((K)

₁₎

_((L)

₁₎

_((H)

₁₎, P_((K)

₁₎

_((L)

₁₎

_((H)

₁₎-P_((K)

₁₎

_((L)

₁₎

_((H)

₁₎ and P_((K)

₁₎

_((L)

₁₎

_((H)

₁₎-P_((K)

₁₎

_((L)

₁₎

_((H)

₁₎ in the outside region 103, each in at least one of the stops W_(N)

_(N)

_(N)-W_((N)

₁₎

_((N)

₁₎

_((N)

₁₎.

Alternatively, one of the probabilities dl₁

₁

₁-dl_(K)

_(L)

_(H) of the event for each of the computation voxels P₁

₁

₁-P_(K)

_(L)

_(H) within the target space 100 nosy be solved from the probabilitydl_(K)

_(L)

_(H) of the event for the computation voxel P_(K)

_(L)

_(H) at a corner of the target space 100 among the right-side,bottom-side and backside borders of the target space 100, as describedin the following method. At the beginning, the probability of the eventfor the computation voxel P_(K)

_(L)

_(H) at the corner of the target space 100 among the right-side,bottom-side and backside borders of the target space 100 may be firstcalculated. Next, the probabilities dl₁

₁

₁dl_((K)

₁₎

_(L)

_(H), dl_(K)

_(L)

₁-dl_(K)

_((L)

₁₎

_(H) and dl_(K)

_(L)

₁-dl_(K)

_(L)

_((H)

₁₎ of the event for the respective computation voxels P₁

₁

₁-P_((K)

₁₎

_(L)

_(H), P_(K)

_(L)

₁-P_(K)

_((L)

₁₎

_(H) and P_(K)

_(L)

₁-P_(K)

_(L)

_((H)

₁₎ within the target space 100 may be solved voxel by voxel from one ofthe probabilities of the event for one of the computation voxels P_(k)

_(l)

_(h) to another probability dl_((k)

₁₎

_(l)

_(h) of the event for another computation voxel P_((k)

₁₎

_(l)

_(h) shifted from said one of the computation voxels P_(k)

_(l)

_(h) by the width X_(fp) of the computation voxels P_(k)

_(l)

_(h) in the leftward direction, from one of the probabilities dl_(k)

_(l)

_(h) of the event for one of the computation voxels P_(k)

_(l)

_(h) to another probability dl_(k)

_((l)

₁₎

_(h) of the event for another computation voxel P_(k)

_((l)

₁₎

_(h) shifted from said one of the computation voxels P_(k)

_(l)

_(h) by the width Y_(fp) of the computation voxels P_(k)

_(l)

_(h) in the upward direction, or from one of the probabilities dl_(k)

_(l)

_(h) of the event for one of the computation voxels P_(k)

_(l)

_(h) to another probability dl_(k)

_(l)

_((h)

₁₎ of the event for another computation voxel P_(k)

_(l)

_((h)

₁₎ shifted from said one of the computation voxels P_(k)

_(l)

_(h) by the width Z_(fp) of the computation voxels P_(k)

_(l)

_(h) in the frontward direction.

V-8 . Probability Map Derived from Measured Values for Stops ofThree-Dimensional Moving Window

Referring to FIGS. 28B, 30A and 30B, in the step S28-5, thethree-dimensional moving window 102 as seen in FIG. 25 may be applied toa three-dimensional space divided into a target space 100 for abiological structure and an outside space 103 for a reference orpredetermined structure such as glass or metal around the target space100 by moving step by step in the three-dimensional space with a shiftequal to a x-direction width X_(fp) of computational voxels P₁

₁

₁-P_((K)

₁₎

_((L)

₁₎

_((H)

₁₎ of a three-dimensional computational map, moving row by row in thethree-dimensional space with a shift equal to a y-direction width Y_(fp)of the computation voxels P₁

₁

₁-P_((K)

₁₎

_((L)

₁₎

_((H)

₁₎ of the three-dimensional computational map and moving plane by planein the three-dimensional space with a shift equal to a z-direction widthZ_(fp) of the computation voxels P₁

₁

₁-P_((K)

₁₎

_((L)

₁₎

_((H)

₁₎ of the three-dimensional computational map to measure one or a set ofvalues C₁

₁

₁-C_((M)

₁₎

_((N)

₁₎

_((U)

₁₎ of one or more imaging parameters, such as parameters of T1, T2 andKtrans for MRI parameters, parameters of T1, T2 and tau for MRIparameters or parameters obtained from a wave penetrating deviceconfigured to generate a wave to penetrate through the target space 100,for each stop W₁

₁

₁-W_((M)

₁₎

_((N)

₁₎

_((U)

₁₎ of the three-dimensional moving window 102. The step S28-5 for movingthe three-dimensional moving window 102 in the path across thecombination of the target and outside spaces 100 and 103 may be referredto the step S27-1 as illustrated in section of V-3 and FIGS. 27A, 30Aand 30B for moving the three-dimensional moving window 102 in the pathacross the combination of the target and outside spaces 100 and 103.Each neighboring two of the stops W₁

₁

₁-W_((M)

₁₎

_((N)

₁₎

_((U)

₁₎ in a x direction may partially overlap with each other with a shiftequal to a x-direction width X_(fp) of the computation voxels P₁

₁

₁-P_((K)

₁₎

_((L)

₁₎

_((H)

₁₎ of the three-dimensional computational map. Each neighboring two ofthe stops W₁

₁

₁-W_((M)

₁₎

_((N)

₁₎

_((U)

₁₎ in a y direction may partially overlap with each other with a shiftequal to a y-direction width Y_(fp) of the computation voxels P₁

₁

₁-P_((K)

₁₎

_((L)

₁₎

_((H)

₁₎ of the three-dimensional computational map. Each neighboring two ofthe stops W₁

₁

₁-W_((M)

₁₎

_((N)

₁₎

_((U)

₁₎ in a z direction may partially overlap with each other with a shiftequal to a z-direction width Z_(fp) of the computation voxels P₁

₁

₁-P_((K)

₁₎

_((L)

₁₎

_((H)

₁₎ of the three-dimensional computational map.

One or more of computed tomography (CT) parameters, positron emissiontomography (PET) parameters, single-photon emission computed tomography(SPECT) parameters, micro-PET parameters, micro-SPECT parameters, Ramanparameters, and/or bioluminescence optical (BLO) parameters, ultrasoundparameters, camera-image parameters and/or visible-light-imageparameters may be measured for the one or the set of values C₁

₁

₁-C_((M)

₁₎

_((N)

₁₎

_((U)

₁₎ for said each stop W₁

₁

₁-W_((M)

₁₎

_((N)

₁₎

_((U)

₁₎ of the three-dimensional moving window. The one or the set of valuesC₁

₁

₁-C_((M)

₁₎

_((N)

₁₎

_((U)

₁₎ of the one or more imaging parameters for said each stop W₁

₁

₁-W_((M)

₁₎

_((N)

₁₎

_((U)

₁₎ of the three-dimensional moving window may be measured from detectionor analysis instruments, such as camera, microscope (optical orelectronic), endoscope, detectors or spectrometer (visible light,fluorescent light, IR, UV or X-ray), ultrasonic machine or system,magnetic resonance imaging (MRI) machine or system, computed tomography(CT) machine or system, positron emission tomography (PET) machine orsystem, single-photon emission computed tomography (SPECT) machine orsystem, micro-PET machine or system, micro-SPECT machine or system,Raman spectrometer or system, and/or bioluminescence optical (BLO)machine or system, or other machine for obtaining molecular orstructural imaging data.

Next, the steps S28-2 through S28-4 as illustrated in FIG. 28A for thefifth aspect continue. Thereby, the algorithm may be employed totransform the one or the set of values C₁

₁

₁-C_((M)

₁₎

_((N)

₁₎

_((U)

₁₎ of the one or more imaging parameters for said each stop W₁

₁

₁-W_((M)

₁₎

_((N)

₁₎

_((U)

₁₎ of the three-dimensional moving window into the probability dl₁

₁

₁-dl_((K)

₁₎

_((L)

₁₎

_((H)

₁₎ of the event for said each computation pixel P₁

₁

₁-P_((K)

₁₎

_((L)

₁₎

_((H)

₁₎ of the three-dimensional computational map having better resolution.

Sixth Aspect: Fixed Value or Probability Set for Computation Pixels orVoxels in Uniform Region or Space of Two-Dimensional orThree-Dimensional Computational Map VI-1. Computational Map Derived fromMeasured Values for Original Pixels of Two-Dimensional Original Map

FIG. 31A illustrates a process of using an E operator to obtain betterresolution of measured values in a two-dimensional region orthree-dimensional space in accordance with an embodiment of the presentapplication. FIG. 33A illustrates a schematic view showing a uniformregion determined in a two-dimensional region in accordance with anembodiment of the present application.

Referring to FIGS. 31A and 33A, the convolution open on (E_(c)) may beperformed as illustrated in the step S23-1 in FIG. 23A for the secondaspect to obtain a value C_(m)

_(n) of the imaging parameter for each stop W_(m)

_(n) of the two-dimensional moving window 2. In an example, referring toFIG. 31A and 33A, the two-dimensional moving window 2 may be shaped witha square having a x-direction width equal to two times of thex-direction width X_(fp) of the computation pixels P_(k)

_(l) and a y-direction width equal to two times of the y-direction widthY_(fp) of the computation pixels P_(k)

_(l). Each of the stops W_(m)

_(n) of the two-dimensional moving window 2 may overlap and beassociated with four of the computation pixels P_(k)

_(l) arranged in 2-by-2 array.

FIGS. 34A-34H are schematically view showing various situations of eachstop W

-W

, W

, W

, W

-W

of the moving window partially overlapping a specific stop W_(m)

_(n) of the moving window. Next, referring to FIG. 31A, 33A and 34A-34H,a step S31-1 may be performed to calculate a difference between thevalue C_(m)

_(n) of the imaging parameter for each stop W_(m)

_(n) and one of the values C

-C

, C

, C

, C

-C

of the imaging parameter for each of its neighboring stops W

-W

, W

, W

, W

-W

partially overlapping said each stop W_(m)

_(n) to the value C_(m)

_(n) of the imaging parameter for said each stop W_(m)

_(n) and calculate a ratio of the difference between the value C_(m)

_(n) of the imaging parameter for each stop W_(m)

_(n) and one of the values C

-C

, C

, C

, C

-C

of the imaging parameter for each of its neighboring stops W

-W

, W

, W

, W

-W

partially overlapping said each stop W_(m)

_(n) to the value C

of the imaging parameter for said each stop W_(m)

_(n).

Next, referring to FIG. 31A, 33A and 34A-34H, a step S31-2 may beperformed to determine if an absolute value of the ratio of thedifference between the value C_(m)

_(n) of the imaging parameter for each stop W_(m)

_(n) and one of the values C

-C

, C

, C

, C

-C

of the imaging parameter for each of its neighboring stops W

-W

, W

, W

, W

-W

partially overlapping said each stop W_(m)

_(n) to the value C_(m)

_(n) of the imaging parameter for said each stop W_(m)

_(n) is smaller than or equal to a threshold value such as 0.1, 0.05 or0.02.

Referring to FIGS. 31A, 33A and 34A-34H, if the absolute value of theratio of the difference between a value C_(m)

_(n) of the imaging parameter for a specific stop W_(m)

_(n) and one of the values C

-C

, C

, C

, C

-C

of the imaging parameter for each of its neighboring stops W

-W

, W

, W

, W

-W

partially overlapping the specific stop W_(m)

_(n) to the value C_(m)

_(n) of the imaging parameter for the specific slop W_(m)

_(n) is determined to be smaller than or equal to the threshold value, astep S31-3 continues to define the two-dimensional computational mapwith a uniform region 110 therein, wherein the uniform region 110 has aprofile defined by a profile of a combination of the specific stop W_(m)

_(n) and each of its neighboring stops W

-W

, W

, W

, W

-W

partially overlapping the specific stop W_(m)

_(n) and to assign or set a constant value of the imaging parameter fora value d_(k)

_(l) of the imaging parameter for each of the computation pixels P_(k)

_(l) in the uniform region 110, wherein the constant value of theimaging parameter is associated with the value C_(m)

_(n) of the imaging parameter for the specific stop W_(m)

_(n) and one of the values C

-C

, C

, C

, C

-C

of the imaging parameter for each of its neighboring stops W

-W

, W

, W

, W

-W

partially overlapping the specific stop W_(m)

_(n), such as an average of the value C_(m)

_(n) of the imaging parameter for the specific stop W_(m)

_(n) and one of the values C

-C

, C

, C

, C

-C

of the imaging parameter for each of its neighboring stops W

-W

, W

, W

, W

-W

partially overlapping the specific stop W_(m)

_(n). For example, the value d_(k)

_(l) of the imaging parameter for said each of the computational pixelsP_(k)

_(l) in the uniform region 110 may be the average multiplied by an areaof said each of the computational pixels P_(k)

_(l). Thus, the value d_(k)

_(l) of the imaging parameter for said each of the computational pixelsP_(k)

_(l) in the uniform region 110 becomes known.

Next, referring to FIGS. 31A, 33A and 34A-34H, a step S31-4 fordeconvolution operation (E_(d)) is performed. In the step S31-4 one ofthe values d_(k)

_(l) of the imaging parameter for each computation pixel P_(k)

_(l) outside the uniform region 110 of the two-dimensional computationalmap is iteratively updated or calculated, as illustrated in the stepsDC1-DC10 in the second aspect, based on one or more of the values C_(m)

_(n) of the imaging parameter for respective one or more of the stopsW_(m)

_(n) each covering said each computation pixel P_(k)

_(l) and/or the common constant value of the imaging parameter for oneor more of the computation pixels P_(k)

_(l) in the uniform region 110 of the two-dimensional computational map,each in at least one of the respective one or more or the stops W_(m)

_(n). Said each computation pixel P_(k)

_(l) has a smaller area than that of each of the respective one or moreof the stops W_(m)

_(n) of the two-dimensional moving window 2. The values d_(k)

_(l) of the imaging parameter for the computation pixels P_(k)

_(l) outside the uniform region 110 are unknown, but the values d_(k)

_(l) of the imaging parameter for the computation pixels P_(k)

_(l) in the uniform region 110 become known. Since the ratio of thenumber of the known values, including the value C_(m)

_(n) of the imaging parameter for each stop W_(m)

_(n) and the values d_(k)

_(l) of the imaging parameter for the computation pixels P_(k)

_(l) in the uniform region 110, to the number of the unknown valuesd_(k)

_(l) of the imaging parameter for the computation pixels P_(k)

_(l) outside the uniform region 110 increases, each of the unknownvalues d_(k)

_(l) of the imaging parameter for the computation pixels P_(k)

_(l) outside the uniform region 110 may be shortly updated into anoptimal value of the imaging parameter by computer iterative computationas mentioned in the second aspect. For example, the value C_(m)

_(n) of the imaging parameter for each stop W_(m)

_(n) of the two-dimensional moving window 2 may be in an unit ofquantity per unit area, and the value d_(k)

_(l) of the imaging parameter for each computation pixel P_(k)

_(l) of the two-dimensional computational map 12 may be total quantityin the area of said each computation pixel P_(k)

_(l).

Referring to FIGS. 31A, 33A and 34A-34H, if none of the uniform region110 is found in the two-dimensional computational map in the step S31-2,a step S31-5 for the deconvolution operation is performed. In the stepS31-5, one of the values d_(k)

_(l) of the imaging parameter for each computation pixel P_(k)

_(l) of the two-dimensional computational map is iteratively updatedcalculated, as illustrated in the steps DC1-DC10 in the second aspect,based on one or more of the values C_(m)

_(n) of the imaging parameter for respective one or more of the stopsW_(m)

_(n) each covering said each computation pixel P_(k)

_(l). For example, the value C_(m)

_(n) of the imaging parameter for each stop W_(m)

_(n) of the two-dimensional moving window 2 may be in a unit of quantityper unit area, and the value d_(k)

_(l) of the imaging parameter for each computation pixel P_(k)

_(l) of the two-dimensional computational map 12 may be total quantityin the area of said each computation pixel P_(k)

_(l).

VI-2. Computational Map Derived from Measured Values for Stops ofTwo-Dimensional Moving Window

Alternatively, FIG. 31B illustrates a process of using an E operator toobtain better resolution of values for pixels or voxels of atwo-dimensional or three-dimensional map in accordance with anotherembodiment of the present application. The process as illustrated inFIG. 31B is the same as that as illustrated in FIG. 31A except that thestep S23-1 is replaced with the step S23-3 as illustrated in FIG. 23Bfor the second aspect. Referring to FIG. 31B, in the step S23-3, thetwo-dimensional moving window 2 may be applied to the target region 11to measure a value C_(m)

_(n) of the imaging parameter for each stop W_(m)

_(n) of the two-dimensional moving window 2.

Next, referring to FIG. 31B, the steps S31-1 through S31-4 asillustrated in FIGS. 31A and 33A and in the section of VI-1 continues orthe steps S31-1, S31-2 and S31-5 as illustrated in FIGS. 31A and 33A andin the section of VI-1 continues.

VI-3. Computational Map Derived from Measured Values for Original Voxelsof Three-Dimensional Original Map

Alternatively, FIG. 33B illustrates a schematic view showing a uniformspace determined in a three-dimensional computational map in accordancewith an embodiment of the present application. Referring to FIGS. 31Aand 33B, the convolution operation (E_(c)) may be performed asillustrated in the step S23-1 in FIG. 23A for the third aspect to obtaina value C_(m)

_(n)

_(u) of the imaging parameter for each stop W_(m)

_(n)

_(u) of the three-dimensional moving window 102. In an example,referring to FIGS. 31A and 33B, the three-dimensional moving window 102may be shaped with a square cube having a x-direction width equal to twotimes of the x-direction width X_(fp) of computation voxels P_(k)

_(l)

_(h) of a three-dimensional computational map, a y-direction width equalto two times of the y-direction width Y_(fp) of the computation voxelsP_(k)

_(l)

_(h) of the three-dimensional computational map and a z-direction widthequal to two times of the z-direction width Z_(fp) of the computationvoxels P_(k)

_(l)

_(h). Each of the stops W_(m)

_(n)

_(u) of the three-dimensional moving window 102 may overlap and beassociated with eight of the computation voxels P_(k)

_(l)

_(h) arranged in 2-by-2-by2 array.

Next, referring to FIG. 31A and 33B, the step S31-1 may be performed tocalculate a difference between the value C_(m)

_(n)

_(u) of the imaging parameter for each stop W_(m)

_(n)

_(u) and one of the values C

-C

, C

-C

, C

-C

, C

, C

, C

-C

of the imaging parameter for each of its neighboring stops W

-W

, W

-W

, W

-W

, W

, W

, W

-W

partially overlapping said each stop W_(m)

_(n)

_(u) to the value C_(m)

_(n)

_(u) of the imaging parameter for said each stop W_(m)

_(n)

_(u) and calculate a ratio of the difference between the value C_(m)

_(n)

_(u) of the imaging parameter for each stop W_(m)

_(n)

_(u) and one of the values C

-C

, C

-C

, C

-C

, C

, C

, C

-C

of the imaging parameter for each of its neighboring stops W

-W

, W

-W

, W

-W

, W

, W

, W

-W

partially overlapping said each stop W_(m)

_(n)

_(u) to the value C_(m)

_(n)

_(u) of the imaging parameter for said each stop W_(m)

_(n)

_(u).

Next, referring to FIG. 31A and 33B, the step S31-2 may be performed todetermine if an absolute value of the ratio of the difference betweenthe value C_(m)

_(n)

_(u) of the imaging parameter for each stop W_(m)

_(n)

_(u) and one of the values C

-C

, C

-C

, C

-C

, C

, C

, C

-C

of the imaging parameter for each of its neighboring stops W

-W

, W

-W

, W

-W

, W

, W

, W

-W

partially overlapping said each stop W_(m)

_(n)

_(u) to the value C_(m)

_(n)

_(u) of the imaging parameter for said each stop W_(m)

_(n)

_(u) is smaller than or equal to a threshold value such as 0.1, 0.05 or0.02.

If the absolute value of the ratio of the difference between a value C

of the imaging parameter for a specific stop W

and one of the values C

-C

, C

-C

, C

-C

, C

, C

, C

-C

of the imaging parameter for each of its neighboring stops W

-W

, W

-W

, W

-W

, W

_(, W)

, W

-W

partially overlapping the specific stop W

to the value C

of the imaging parameter for the specific stop W

is determined to be smaller than or equal to the threshold value, thestep S31-3 continues to define the three-dimensional computational mapwith a uniform space 110 therein, wherein the uniform space 110 has aprofile defined by a profile of a combination of the specific stop W_(m)

_(n)

_(u) and each of its neighboring stops W

-W

, W

-W

, W

-W

, W

, W

, W

-W

partially overlapping the specific stop W

, and to assign or set a constant value of the imaging parameter for avalue d_(k)

_(l)

_(h) of the imaging parameter for each of the computation voxels, e.g.,P

, in the uniform space 110, wherein the constant value of the imagingparameter is associated with the value C

of the imaging parameter for the specific stop W

and one of the values C

-C

, C

-C

, C

-C

, C

, C

, C

-C

of the imaging parameter for each of its neighboring stops W

-W

, W

-W

, W

-W

, W

, W

, W

-W

partially overlapping the specific stop W

such as an average of the value C

of the imaging parameter for the specific stop W

and one of the values C

-C

, C

-C

, C

-C

, C

, C

, C

-C

of the imaging parameter for each of its neighboring stops W

-W

, W

-W

, W

-W

, W

, W

, W

-W

partially overlapping the specific stop W

.

Next, referring to FIGS. 31A and 33B, the step S31-4 for thedeconvolution operation (E_(d)) is performed. In the step S31-4, one ofthe values d_(k)

_(l)

_(h) of the imaging parameter for each computation voxel P_(k)

_(l)

_(h) outside the uniform space 110 of the three-dimensionalcomputational map is iteratively updated or calculated, as illustratedin the steps DC1-DC10 in the third aspect, based on one or more of thevalues C_(m)

_(n)

_(u) of the imaging parameter for respective one or more of the stopsW_(m)

_(n)

_(u) each covering said each computation voxel P_(k)

_(l)

_(h) and/or the constant value of the imaging parameter for one or moreof the computation voxels in the uniform space 110 of thethree-dimensional computational map, each in at least one of therespective one or more of the stops W_(m)

_(n)

_(u). Said each computation voxel P_(k)

_(l)

_(h) has a smaller area than that of each of the respective one or moreof the stops W_(m)

_(n)

_(u) of the three-dimensional moving window 102. The values d_(k)

_(l)

_(h) of the imaging parameter for the computation voxels P_(k)

_(l)

_(h) outside the uniform space 110 are unknown, but the values, e.g. d

, of the imaging parameter for the computation voxels, e.g. P

, in the uniform space 110 become known. Since the ratio of the numberof the known values, including the value C_(m)

_(n)

_(u) of the imaging parameter for each stop W_(m)

_(n)

_(u) and the values, e.g. d

, of the imaging parameter for the computation voxels, e.g. P

, in the uniform space 110, to the number of the unknown values d_(k)

_(l)

_(h) of the imaging parameter for the computation voxels P_(k)

_(l)

_(h) outside the uniform space 110 increases, each of the unknown valuesd_(k)

_(l)

_(h) of the imaging parameter for the computation voxels P_(k)

_(l)

_(h) outside the uniform space 110 may be shortly updated into anoptimal value of the imaging parameter by computer iterative computationas mentioned in the third aspect.

If none of the uniform space 110 is found in the three-dimensionalcomputational map in the step S31-2, the step S31-5 for thedeconvolution operation is performed. In the step S31-5, one of thevalues d_(k)

_(l)

_(h) of the imaging parameter for each computation voxel P_(k)

_(l)

_(h) of the three-dimensional computational map is iteratively updatedor calculated, as illustrated in the steps DC1-DC10 in the third aspect,based on one or more of the values C_(m)

_(n)

_(u) of the imaging parameter for respective one or more of the stopsW_(m)

_(n)

_(u) each covering said each computation voxel P_(k)

_(l)

_(h).

VI-4. Computational Map Derived from Measured Values for Stops ofThree-Dimensional Moving Window

The process as illustrated in FIG. 31B is the same as that asillustrated in FIG. 31A except that the step S23-1 is replaced with thestep S23-3 as illustrated in FIG. 23B for the third aspect. Referring toFIG. 31B, in the step S23-3, the three-dimensional moving window 102 maybe applied to the target space 100 to measure a value C_(m)

_(n)

_(u) of the imaging parameter for each stop W_(m)

_(n)

_(u) of the third-dimensional moving window 102.

Next, referring to FIG. 31B, the steps S31-1 through S31-4 asillustrated in FIGS. 31A and 33B and in the section of VI-3 continues orthe steps S31-1, S31-2 and S31-5 as illustrated in FIGS. 31A and 33B andin the section of VI-3 continues.

VI-5. Summary for Sections VI-3 and VI-4

Follow the section III-3 for Summary of Third Aspect, referring to FIGS.31A and 31B, the method further includes: (1) providing, by the imagingsystem, a fifth stop, e.g. W

in FIG. 33B, of the stops, e.g. W₁

₁

₁-W_(N)

_(N)

_(N) in FIGS. 26A-26C and 33B, of the three-dimensional moving window102 covering a second computation voxel, e.g. P

in FIG. 33B, wherein the second computation voxel, e.g. P

in FIG. 33B, is another three-dimensional unit of the three-dimensionalcomputational map, having the first dimension X_(fp) in the firstdirection, e.g. X direction, the second dimension Y_(fp) in the seconddirection, e.g. Y direction, and the third dimension Z_(fp) in the thirddirection, e.g. Z direction; (2) for the step S31-1, calculating, by theimaging system, a difference between the first value, e.g. C

, for the fifth stop, e.g. W

in FIG. 33B, and the first value, e.g. C

, for each of all its neighboring stops, e.g. W

in FIG. 33B, of the three-dimensional moving window 102, partiallyoverlapping the fifth stop, e.g. W

in FIG. 33B, of the three-dimensional moving window 102; (3) for thestep 31-1, calculating, by the imaging system, a ratio of each of thedifferences to the first value, e.g. C

, for the fifth stop, e.g. W

in FIG. 33B, of the three-dimensional moving window 102; (4) for thestep S31-2, determining, by the imaging system, if each of absolutevalues of the ratios is less than or equal to a threshold value; (5) forthe step S31-3, defining, by the imaging system, a space covered by thefifth stop, e.g. W

in FIG. 33B, and all its neighboring stops, e.g. W

in FIG. 33B, partially overlapping the fifth stop, e.g. in FIG. 33B, ofthe three-dimensional moving window 102 as a uniform space 110, whereinthe second computation voxel, e.g. P

in FIG. 33B, is in the uniform space 110; (6) for the step S32-3,assigning, by the imaging system, a constant value of the imagingparameter for the second computation voxel, e.g. P

in FIG. 33B, wherein the constant value is associated with the firstvalue, e.g. C

, for the fifth stop, e.g. W

in FIG. 33B, and the first values, e.g. C

, for all its neighboring stops, e.g. W

in FIG. 33B, partially overlapping the fifth stop, e.g. W

in FIG. 33B, of the three-dimensional moving window 102; and (7) for thestep S32-3, assigning, by the imaging system, the constant value foreach of other computation voxels, e.g. P

in FIG. 33B, other than the second computation voxel, e.g. P

in FIG. 33B, in the uniform space 110.

Furthermore, for the step S32-4, the method includes said calculatingthe second value. e.g. d_(k)

_(l)

_(h), for the first computation voxel, e.g. P_(k)

_(l)

_(h) in FIGS. 26D-26F and 33C, as described in the section IV-3 forSummary for Fourth Aspect, based on further information associated witha third value of the imaging parameter for a sixth stop, e.g. W

in FIGS. 26G and 33C, of the stops, e.g. W₁

₁

₁-W_(N)

_(N)

_(N) in FIGS. 26A-26C, of the three-dimensional moving window 102partially overlapping the uniform space 110, wherein the third value forthe sixth stop, e.g. W

in FIGS. 26G and 33C, of the three-dimensional moving window 102 iscalculated based on information associated with the constant value foreach computation voxel, e.g. P

in FIG. 33C, in the uniform space 110 and in the sixth stop, e.g. W

in FIGS. 26G and 33C.

Furthermore, for the step S31-4, said calculating the second value, e.g.d_(k)

_(l)

_(h) for the first computation voxel, e.g. P_(k)

_(l)

_(h) in FIGS. 26D-26F, 33C and 33D, includes: (1) calculating, by theimaging system, a first assumed value of the imaging parameter for thefirst computation voxel, e.g. P_(k)

_(l)

_(h) in FIGS. 26D-26F, 33C and 33D, based on information associated withthe first values, e.g., C_(m)

_(n)

_(u), C

, C

and C

for the first through fourth stops, e.g., W_(m)

_(n)

_(u), W

, W

and W

in FIGS. 26D-26F and 33D, of the three-dimensional moving window 102;(2) calculating, by the imaging system, a second assumed value of theimaging parameter for each of other computation voxels, e.g. P

, P

and P

in FIG. 33D, other than the first computation voxel, in each of thefirst through fourth stops, e.g. W_(m)

_(n)

_(u), W

, W

, and W

in FIGS. 26D-26F and 33D, wherein said calculating the second assumedvalue for a voxel, e.g. P

, P

or P

in FIG. 33D, of the other computation voxels in each of the firstthrough fourth stops, e.g., W_(m)

_(n)

_(u), W

, W

, and W

in FIGS. 26D-26F and 33D, is based on information associated with thefirst value, e.g. C_(m)

_(n)

_(u) and/or C

, for each of the stops, e.g. W_(m)

_(n)

_(u) and/or W

in FIG. 33D, of the three-dimensional moving window 102 covering thevoxel, e.g. P

, P

or P

in FIG. 33D, of the other computation voxels; (3) calculating, by theimaging system, a first value guess of the imaging parameter for acertain stop, e.g. W

in FIGS. 26D and 33D, of the first through fourth stops of thethree-dimensional moving window partially overlapping the uniform space110 based on information associated with the first assumed value for thefirst computation voxel, e.g. P_(k)

_(l)

_(h) in FIGS. 26D-26F, 33C and 33D, the second assumed value for each ofthe other computation voxels, e.g. P

in FIG. 33D, in the certain stop, e.g. W

in FIGS. 26D and 33D, and outside the uniform space 110 and the constantvalue for the other computation voxels, e.g. P

in FIG. 33D, in the certain stop, e.g. W

in FIGS. 26D and 33D, and in the uniform space 110; (4) calculating, bythe imaging system, a second value guess of the imaging parameter foreach of other stops, e.g. W_(m)

_(n)

_(u) in FIGS. 26D-26F and 33D, other than the certain stop, of the firstthrough fourth stops not overlapping the uniform space 110, wherein saidcalculating the second value guess for a stop, e.g. W_(m)

_(n)

_(u) in FIGS. 26D-26F and 33D, of the other stops of the first throughfourth stops not overlapping the uniform space 110 is based oninformation associated with the first assumed value for the firstcomputation voxel, e.g. P_(k)

_(l)

_(h) in FIGS. 26D-26F, 33C and 33D, and the second assumed value foreach of the other computation voxels, e.g. P

in FIG. 33D, outside the uniform space 110 and in the stop, e.g. W_(m)

_(n)

_(u) in FIGS. 26D-26F and 33D, of the other stops; (5) calculating, bythe imaging system, a first difference between the first value guess andthe first value, e.g. C

for the certain stop, e.g. W

in FIGS. 26D and 33D; (6) calculating, by the imaging system, a seconddifference between the second value guess and the first value, e.g.C_(m)

_(n)

_(u) for each of the other stops, e.g. W_(m)

_(n)

_(u) in FIGS. 26D-26F and 33D, of the first through fourth stops notoverlapping the uniform space 110, and (7) updating, by the imagingsystem, the first assumed value for the first computation voxel, e.g.P_(k)

_(l)

_(h) in FIGS. 26D-26F, 33C and 33D, based on information associated withthe first difference and the second differences for the first throughfourth stops, e.g. W_(m)

_(n)

_(u), W

, W

and W

in FIGS. 26D-26F and 33D, of the three-dimensional moving window 102.

VI-6. Probability Map Derived from Measured Values for Original Pixelsof Two-Dimensional Original Map

FIG. 32A illustrates a process of using an E operator to obtain betterresolution of probabilities of an event for pixels or voxels of atwo-dimensional or three-dimensional probability map in accordance withan embodiment of the present application. Referring to FIGS. 32A and33A, the convolution operation (E_(c)) may be performed as illustratedin the step S22-1 in FIG. 22A for the first aspect to obtain one or aset of values C_(m)

_(n)

_(u) of the one or more imaging parameters for each stop W_(m)

_(n) of the two-dimensional moving window 2. In an example, referring toFIGS. 32A and 33A, the two-dimensional moving window 2 may be shapedwith a square having a x-direction width equal to two times of thex-direction width X_(fp) of the computation pixels P_(k)

_(l) and a y-direction width equal to two times of the y-direction widthY_(fp) of the computation pixels P_(k)

_(l). Each of the stops W_(m)

_(n) of the two-dimensional moving window 2 may overlap and beassociated with four of the computation pixels P_(k)

_(l) arranged in 2-by-2 array.

Next, referring to FIGS. 32A and 33A, the step S22-2 for big-dataengineering learning may be performed as illustrated in FIG. 22A for thefirst aspect to calculate or obtain a probability CL_(m)

_(n) of an event for each stop W_(m)

_(n) by matching the one or the set of values C_(m)

_(n) of the one or more imaging parameters for said each stop W_(m)

_(n) of the two-dimensional moving window 2 to a classifier such asBayesian classifier.

Next, referring to FIG. 32A, 33A and 34A-34H, a step S32-1 may beperformed to calculate a difference between the probability CL_(m)

_(n) of the event for each stop W_(m)

_(n) and one of the probabilities CL

-CL

, CL

, CL

, CL

-CL

of the event for each of its neighboring stops W

-W

, W

, W

, W

-W

partially overlapping said each stop W_(m)

_(n) to the probability CL_(m)

_(n) of the event for said each stop W_(m)

_(n) and calculate a ratio of the difference between the probabilityCL_(m)

_(n) of the event for each stop W_(m)

_(n) and one of the probabilities CL

-CL

, CL

, CL

, CL

-CL

of the event for each of its neighboring stops W

-W

, W

, W

, W

-W

partially overlapping said each stop W_(m)

_(n) to the probability CL_(m)

_(n) of the event for said each stop W_(m)

_(n).

Next, referring to FIG. 32A, 33A and 34A-34H, a step S32-2 may beperformed to determine if an absolute value of the ratio of thedifference between the probability CL_(m)

_(n) of the event for each stop W_(m)

_(n) and one of the probabilities CL

-CL

, CL

, CL

, CL

-CL

of the event for each of its neighboring stops W

-W

, W

, W

, W

-W

partially overlapping said each stop W_(m)

_(n) to the probability CL_(m)

_(n) of the event for said each stop W_(m)

_(n) is smaller than or equal to a threshold value such as 0.1, 0.05 or0.02.

Referring to FIGS. 32A, 33A and 34A-34H, if the absolute value of theratio of the difference between a probability CL_(m)

_(n) of the event for a specific stop W_(m)

_(n) and one of the probabilities CL

-CL

, CL

, CL

, CL

-CL

of the event for each of its neighboring stops W

-W

, W

, W

, W

-W

partially overlapping the specific stop W_(m)

_(n) to the probability CL_(m)

_(n) of the event for the specific stop W_(m)

_(n) is determined to be smaller than or equal to the threshold value, astep S32-3 continues to define the two-dimensional computational mapwith a uniform region 110 therein, wherein the uniform region 110 has aprofile defined by a profile of a combination of the specific stop W_(m)

_(n) and each of its neighboring stops W

-W

, W

, W

, W

-W

partially overlapping the specific stop W_(m)

_(n) and to assign or set a constant probability of the event for aprobability dl_(k)

_(l) of the event for each of the computation pixels P_(k)

_(l) in the uniform region 110, wherein the constant probability of theevent is associated with the probability CL_(m)

_(n) of the event for the specific stop W_(m)

_(n) and one of the probabilities CL

-CL

, CL

, CL

, CL

-CL

of the event for each of its neighboring stops W

-W

, W

, W

, W

-W

partially overlapping the specific stop W_(m)

_(n), such as an average of the probability CL_(m)

_(n) of the event for the specific stop W_(m)

_(n) and one of the probabilities CL

-CL

, CL

, CL

, CL

-CL

of the event for each of its neighboring W

-W

, W

, W

, W

-W

partially overlapping the specific stop W_(m)

_(n).

Next, referring to FIGS. 32A, 33A and 34A-34H, a step S32-4 fordeconvolution operation (E_(d)) is performed. In the step S32-3, one ofthe probabilities dl_(k)

_(l) of the event for each computation pixel P_(k)

_(l) outside the uniform region 110 of the two-dimensional computationalmap is iteratively updated or calculated, as illustrated in the stepsST1-ST11 in the first aspect, based on one or more of the probabilitiesCL_(m)

_(n) of the event for respective one or more of the stops W_(m)

_(n) each covering said each computation pixel P_(k)

_(l) and/or the common constant probability of the event for one or moreof the computation pixels P_(k)

_(l) in the uniform region 110 of the two-dimensional computational map,each in at least one of the respective one or more of the stops W_(m)

_(n). Said each computation pixel P_(k)

_(l) has a smaller area than that of each of the respective one or moreof the stops W_(m)

_(n) of the two-dimensional moving window 2. The probabilities dl_(k)

_(l) of the event for the computation pixels P_(k)

_(l) outside the uniform region 110 are unknown, but the probabilitiesdl_(k)

_(l) of the event for the computation pixels P_(k)

_(l) in the uniform region 110 become known. Since the ratio of thenumber of the known probabilities of the event, including theprobability CL_(m)

_(n) of the event for each stop W_(m)

_(n) and the probabilities dl_(k)

_(l) of the event for the computation pixels P_(k)

_(l) in the uniform region 110, to the number of the unknownprobabilities dl_(k)

_(l) of the event for the computation pixels P_(k)

_(l) outside the uniform region 110 increases, each of the unknownprobabilities dl_(k)

_(l) of the event for the computation pixels P_(k)

_(l) outside the uniform region 110 may be shortly updated into anoptimal probability of the event by computer iterative computation asmentioned in the first aspect.

Referring to FIGS. 32A, 33A and 34A-34H, if none of the uniform region110 is found in the two-dimensional computational map in the step S32-2,a step S32-5 for the deconvolution operation is performed. In the stepS32-5, one of the probabilities dl_(k)

_(l) of the event for each computation pixel P_(k)

_(l) of the two-dimensional computational map is iteratively updated orcalculated, as illustrated in the steps ST1-ST11 in the first aspect,based on one or more of the probabilities CL_(m)

_(n) of the event for respective one or more of the stops W_(m)

_(n) each covering said each computation pixel P_(k)

_(l).

VI-7. Probability Map Derived from Measured Values for Stops ofTwo-Dimensional Moving Window

Alternatively, FIG. 32B illustrates a process of using an operator toobtain better resolution of probabilities of an event for pixels orvoxels of a two-dimensional or three-dimensional probability map inaccordance with another embodiment of the present application. Theprocess as illustrated in FIG. 32B is the same as that as illustrated inFIG. 32A except that the step S22-1 is replaced with the step S22-4 asillustrated in FIG. 22B for the first aspect. Referring to FIG. 32B, inthe step S22-4, the two-dimensional moving window 2 may be applied tothe target region 11 to measure one or a set of values C_(m)

_(n) of the one or more imaging parameters for each stop W_(m)

_(n) of the two-dimensional moving window 2.

Next, referring to FIG. 32B, the steps S22-2 and S32-1 through S32-4 asillustrated in FIGS. 32A and 33A and in the section of VI-5 continues orthe steps S22-2, S32-1, S32-2 and S32-5 as illustrated in FIGS. 32A and33A and in the section of VI-5 continues.

VI-8. Probability Map Derived from Measured Values for Original Voxelsof Three-dimensional Original Map

Referring to FIGS. 32A and 33B, the convolution operation (E_(c)) may beperformed as illustrated in the step S22-1 in FIG. 22A for the fourthaspect to obtain one or a set of value C_(m)

_(n)

_(u) of the one or more imaging parameters for each stop W_(m)

_(n)

_(u) of the three-dimensional moving window 102. In an example,referring to FIGS. 32A and 33B, the three-dimensional moving window 102may be shaped with a square cube having a x-direction width equal to twolines of the x-direction width X_(fp) or computation voxels P_(k)

_(l)

_(h) of a three-dimensional computational map, a y-direction width equalto two lines of the y-direction width Y_(fp) of the computation voxelsP_(k)

_(l)

_(h) of the three-dimensional computational map and a z-direction widthequal to two times of the z-direction width Z_(fp) of the computationvoxels P_(k)

_(l)

_(h). Each of the stops W_(m)

_(n)

_(u) of the three-dimensional moving window 102 may overlap and beassociated with eight of the computation voxels P_(k)

_(l)

_(h) arranged in 2-by-2-by2 array.

Next, referring to FIGS. 32A and 33B, the step S22-2 for big-dataengineering learning may be performed as illustrated in FIG. 22A for thefourth aspect to calculate or obtain a probability CL_(m)

_(n)

_(u) of an event for each stop W_(m)

_(n)

_(u) by matching the one or the set of values C_(m)

_(n)

_(u) of the one or more imaging parameters for said each stop W_(m)

_(n)

_(u) of the three-dimensional moving window 102 to a classifier such asBayesian classifier.

Next, referring to FIG. 32A and 33B, the step S32-1 may be performed tocalculate a difference between the probability CL_(m)

_(n)

_(u) of the event for each stop W_(m)

_(n)

_(u) and one of the probabilities CL

-CL

, CL

-CL

, CL

-CL

, CL

, CL

, CL

-CL

of the event for each of its neighboring stops W

-W

, W

-W

, W

-W

, W

, W

, W

-W

partially overlapping said each stop W_(m)

_(n)

_(u) and calculate a ratio of the difference between the probabilityCL_(m)

_(n)

_(u) of the event for each stop W_(m)

_(n)

_(u) and one of the probabilities CL

-CL

, CL

-CL

, CL

-CL

, CL

, CL

, CL

-CL

of the event for each of its neighboring stops W

-W

, W

-W

, W

-W

, W

, W

, W

-W

partially overlapping said each stop W_(m)

_(n)

_(u).

Next, referring to FIG. 32A and 33B, the step S32-2 may be performed todetermine if an absolute value of the ratio of the difference betweenthe probability CL_(m)

_(n)

_(u) of the event for each stop W_(m)

_(n)

_(u) and one of the probabilities CL

-CL

, CL

-CL

, CL

-CL

, CL

, CL

, CL

-CL

of the event for each of its neighboring stops W

-W

, W

-W

, W

-W

, W

, W

, W

-W

partially overlapping said each stop W_(m)

_(n)

_(u) to the probability CL_(m)

_(n)

_(u) of the event for said each stop W_(m)

_(n)

_(u) is smaller than or equal to a threshold value such as 0.1, 0.05 or0.02.

Referring to FIG. 32A and 33B, if the absolute value of the ratio of thedifference between a probability CL

of the event fora specific stop W

and one of the probabilities CL

-CL

, CL

-CL

, CL

-CL

, CL

, CL

, CL

-CL

of the event for each of its neighboring stops W

-W

, W

-W

, W

-W

, W

, W

, W

-W

partially overlapping the specific stop W

to the probability CL

of the event for the specific stop W

is determined to be smaller than or equal to the threshold value, thestep S32-3 continues to define the three-dimensional computational mapwith a uniform space 110 therein, wherein the uniform space 110 has aprofile defined by a profile of a combination of the specific stop W

and each of its neighboring stops W

-W

, W

-W

, W

-W

, W

, W

, W

-W

partially overlapping the specific stop W

, and to assign or set a constant probability of the event for aprobability, e.g. dl

, of the event for each of the computation voxels, e.g. P

in the uniform space 110, wherein the constant probability of the eventis calculated based on information associated with the probability CL

of the event for the specific stop W

and one of the probabilities CL

-CL

, CL

-CL

, CL

-CL

, CL

, CL

, CL

-CL

of the event for each of its neighboring stops W

-W

, W

-W

, W

-W

, W

, W

, W

-W

partially overlapping the specific stop W

, such as an average of the probability CL

of the event for the specific stop W

and one of the probabilities CL

-CL

, CL

-CL

, CL

-CL

, CL

, CL

, CL

-CL

of the event for each of its neighboring stops W

-W

, W

-W

, W

-W

, W

, W

, W

-W

partially overlapping the specific stop W

.

Next, referring to FIGS. 32A and 33B, the step S32-4 for thedeconvolution operation (E_(d)) is performed. In the step S32-4, one ofthe probabilities dl_(k)

_(l)

_(h) of the event or each computation voxel outside the uniform space110 of the three-dimensional computational map is iteratively updated orcalculated, as illustrated in the steps DL1-DL10 in the fourth aspect,based on one or more of the probabilities CL_(m)

_(n)

_(u) of the event for respective one or more of the stops each coveringsaid each computation voxel P_(k)

_(l)

_(h) and/or the constant probability of the event for one or more of thecomputation voxels in the uniform space 110 of the three-dimensionalcomputational map, each in at least one of the respective one or more ofthe stops W_(m)

_(n)

_(u). Said each computation voxel P_(k)

_(l)

_(h) has a smaller area than that of each of the respective one or moreof the stops W_(m)

_(n)

_(u) of the three-dimensional moving window 102. The probabilitiesdl_(k)

_(l)

_(h) of the event for the computation voxels P_(k)

_(l)

_(h) outside the uniform space 110 are unknown, but the probabilities,e.g. dl

, of the event for the computation voxels, e.g. P

, in the uniform space 110 become known. Since the ratio of the numberof the known probabilities of the event, including the probability CL

of the event for each stop W_(m)

_(n)

_(u) and the probabilities, e.g. dl

, of the event for the computation voxels, e.g. P

, in the uniform space 110, to the number of the unknown probabilitiesdl

of the event for the computation voxels P_(k)

_(l)

_(h) outside the uniform space 110 increases, each of the unknownprobabilities of the event for the computation voxels P_(k)

_(l)

_(h) outside the uniform space 110 may be shortly updated into anoptimal probability of the event by computer iterative computation asmentioned in the fourth aspect.

Referring to FIG. 32A and 33B, if none of the uniform space 110 is foundin the three-dimensional computational map in the step S32-2, the stepS32-5 for the deconvolution operation is performed. In the step S32-5.one of the probabilities dl_(k)

_(l)

_(h) of the event for each computation voxel P_(k)

_(l)

_(h) of the three-dimensional computational map is iteratively updatedor calculated, as illustrated in the steps DL1-DL10 in the fourthaspect, based on one or more of the probabilities CL_(m)

_(n)

_(u) of the event for respective one or more of the stops W_(m)

_(n)

_(u) each covering said each computation voxel P_(k)

_(l)

_(h).

VI-9. Probability Map Derived from Measured Values for Stops ofThree-Dimensional Moving Window

The process as illustrated in FIG. 32B is the same as that asillustrated in FIG. 32A except that the step S22-1 is replaced with thestep S22-4 as illustrated in FIG. 22B for the fourth aspect. Referringto FIG. 31B, in the step S22-4, the three-dimensional moving window 102may be applied to the target space 100 to measure one or a set of valuesC_(m)

_(n)

_(u) of the one or more imaging parameters for each stop W_(m)

_(n)

_(u) of the third-dimensional moving window 102.

Next, referring to FIG. 32B, the steps S22-2 and S32-1 through S32-4 asillustrated in FIGS. 32A and 33B and in the section of VI-7 continues orthe steps S22-2, S32-1, S32-2 and S32-5 as illustrated in FIGS. 32A and33B and in the section of VI-7 continues.

VI-10 Summary for Sections VI-8 and VI-9

Following the section IV-3 for Summary of Fourth Aspect, referring toFIGS. 32A and 32B, the method further includes: (1) providing, by theimaging system, a fifth stop, e.g. W

in FIG. 33B, of the stops, e.g. W₁

₁

₁-W_(N)

_(N)

_(N) in FIGS. 26A-26C and 33B, of the three-dimensional moving window102 covering a second computation voxel, e.g. P

in FIG. 33B, wherein the second computation voxel, e.g. P

in FIG. 33B, is another three-dimensional unit of the three-dimensionalprobability map, having the first dimension X_(fp) in the firstdirection, e.g. X direction, the second dimension Y_(fp) in the seconddirection, e.g. Y direction, and the third dimension Z_(fp) in the thirddirection, e.g. Z direction; (2) for the step S32-1, calculating, by theimaging system, a difference between the firm probability, e.g. CL

, of the event for the fifth stop, e.g. W

in FIG. 33B, and the first probability, e.g. CL

, of the event for each of all its neighboring stops, e.g. W

in FIG. 33B, of the three-dimensional moving window 102, partiallyoverlapping the fifth stop, e.g. W

in FIG. 33B, of the three-dimensional moving window 102, (3) for thestep 32-1, calculating, by the imaging system, a ratio of each of thedifferences to the first probability, e.g. CL

, of the event for the fifth stop, e.g. W

in FIG. 33B, of the three-dimensional moving window 102; (4) for thestep S32-2, determining, by the imaging system, if each of absolutevalues of the ratios is less than or equal to a threshold value; (5) forthe step S32-3, defining, by the imaging system, a space covered by thefifth stop, e.g. W

in FIG. 33B, and all its neighboring stops, e.g. W

in FIG. 33B, partially overlapping the fifth stop, e.g. W

in FIG. 33B, of the three-dimensional moving window 102 as a uniformspace 110, wherein the second computation voxel, e.g. P

in FIG. 33B, is in the uniform space 110; (6) for the step S32-3,assigning, by the imaging system, a constant probability of the eventfor the second computation voxel, e.g. P

in FIG. 33B, wherein the constant probability of the event is associatedwith the first probability, e.g. CL

, of the event for the fifth stop, e.g. W

in FIG. 33B, and the first probabilities, e.g. CL

, of the event for all its neighboring stops, e.g. W

in FIG. 33B, partially overlapping the fifth stop, e.g. W

in FIG. 33B, of the three-dimensional moving window 102; and (7) for thestep S32-3, assigning, by the imaging system, the constant probabilityof the event for each of other computation voxels, e.g. P

in FIG. 33B, other than the second computation voxel, e.g. P

in FIG. 33B, in the uniform space 110.

Furthermore, for the step S32-4, the method includes said calculatingthe second probability, e.g. dl_(k)

_(l)

_(h), of the event for the first computation voxel, e.g. P_(k)

_(l)

_(h) in FIGS. 26D-26F and 33C, as described in the section IV-3 forSummary for Fourth Aspect, based on further information associated witha third probability of the event for a sixth stop, e.g. W

in FIGS. 26G and 33C, of the stops, e.g. W₁

₁

₁-W_(N)

_(N)

_(N) in FIGS. 26A-26C, of the three-dimensional moving window 102partially overlapping the uniform space 110, wherein the thirdprobability of the event for the sixth stop, e.g. W

in FIGS. 26G and 33C, of the three-dimensional moving window 102 iscalculated based on information associated with the constant probabilityof the event for each computation voxel, e.g. P

in FIG. 33C, in the uniform space 110 and in the sixth stop, e.g. W

in FIGS. 26G and 33C.

Furthermore, for the step S32-4, said calculating the secondprobability, e.g. dl_(k)

_(l)

_(h), of the event for the first computation voxel, e.g. P_(k)

_(l)

_(h) in FIGS. 26D-26F, 33C and 33D, includes: (1) calculating, by theimaging system, a first assumed probability of the event for the firstcomputation voxel, e.g. P_(k)

_(l)

_(h) in FIGS. 26D-26F, 33C and 33D, based on information associated withthe first probabilities, e.g., CL_(m)

_(n)

_(u), CL

, CL

and CL

, of the event for the first through fourth stops, e.g. W_(m)

_(n)

_(u), W

, W

and W

in FIGS. 26D-26F and 33D, of the three-dimensional moving window 102;(2) calculating, by the imaging system, a second assumed probability ofthe event for each of other computation voxels, e.g. P

, P

and P

in FIG. 33D, other than the first computation voxel, in each of thefirst through fourth stops, e.g., W_(m)

_(n)

_(u), W

, W

and W

in FIGS. 26D-26F and 33D, wherein said calculating the second assumedprobability of the event for a voxel, e.g. P

, P

or P

in FIG. 33D, of the other computation voxels in each of the firstthrough fourth stops, e.g., W_(m)

_(n)

_(u), W

, W

and W

in FIGS. 26D-26F and 33D, is based on information associated with thefirst probability, e.g. CL_(m)

_(n)

_(u) and/or CL

of the event for each of the stops, e.g. W_(m)

_(n)

_(u) and/or in FIG. 33D, of the three-dimensional moving window 102covering the voxel, e.g. P

, P

or P

in FIG. 33D, of the other computation voxels; (3) calculating, by theimaging system, a first probability guess of the event for a certainstop, e.g. W_(/) in FIGS. 26D and 33D, of the first through fourth stopsof the three-dimensional moving window partially overlapping the uniformspace 110 based on information associated with the first assumedprobability of the event for the first computation voxel, e.g. P_(k)

_(l)

_(h) in FIGS. 26D-26F, 33C and 33D, the second assumed probability ofthe event for each of the other computation voxels, e.g. P

in FIG. 33D, in the certain stop, e.g. W

in FIGS. 26D and 33D, and outside the uniform space 110 and the constantprobability of the event for the other computation voxels, e.g. P

in FIG. 33D, in the certain stop, e.g. W

in FIGS. 26D and 33D, and in the uniform space 110; (4) calculating, bythe imaging system, a second probability guess of the event for each ofother stops, e.g. W_(m)

_(n)

_(u) in FIGS. 26D-26F and 33D, other than the certain stop, of the firstthrough fourth stops not overlapping the uniform space 110, wherein saidcalculating the second probability guess of the event for a stop, e.g.W_(m)

_(n)

_(u) in FIGS. 26D-26F and 33D, of the other stops of the first throughfourth stops not overlapping the uniform space 110 is based oninformation associated with the first assumed probability of the eventfor the first computation voxel, e.g. P_(k)

_(l)

_(h) in FIGS. 26D-26F, 33C and 33D, and the second assumed probabilityof the event for each of the other computation voxels, e.g. P

in FIG. 33D, outside the uniform space 110 and in the stop, e.g. W_(m)

_(n)

_(u) in FIGS. 26D-26F and 33D, of the other stops; (5) calculating, bythe imaging system, a first difference between the first probabilityguess of the event and the first probability, e.g. CL

of the event for the certain stop, e.g. W

in FIGS. 26D and 33D; (6) calculating, by the imaging system, a seconddifference between the second probability guess of the event and thefirst probability, e.g. CL_(m)

_(n)

_(u), of the event for each of the other stops, e.g. W_(m)

_(n)

_(u) in FIGS. 26D-26F and 33D, of the first through fourth stops notoverlapping the uniform space 110; and (7) updating, by the imagingsystem, the first assumed probability of the event for the firstcomputation voxel, e.g. P_(k)

_(l)

_(h) in FIGS. 26D-26F, 33C and 33D, based on information associated withthe first difference and the second differences for the first throughfourth stops, e.g. W_(m)

_(n)

_(u), W

, W

and W

in FIGS. 26D-26F and 33D, of the three-dimensional moving window 102.

Seventh Aspect: Multiple Measuring Pixels of Two-dimensional MovingWindow

Alternatively, FIG. 35A is a schematic view showing a two-dimensionalmoving window provided with four measuring pixels arranged in a 2-by-2array in accordance with an example of the present application. FIG. 35Bis a schematic view showing a measuring pixel of a two-dimensionalmoving window has a profile defined by a profile of a combination ofnine computation pixels, arranged in a 3-by-3 array, of atwo-dimensional computational map in accordance with an example of thepresent application. Referring to FIG. 35A, a two-dimensional movingwindow 2 may whole multiple measuring pixels 20 arranged in anM_(mp)-by-N_(mp) array therein, wherein the number of “M

” may be an integer greater than or equal to 1, such as 2, 3 or 4, andthe number of “N_(mp)” may be an integer greater than or equal is 1,such as 2, 3 or 4. In this case, the number of “M

” is equal to 2 and the number “N_(mp)” is equal to 2, as seen in FIG.35A. The two-dimensional moving window 2 may be applied to the targetregion 11 for the step S22-4 or S23-3 in the first, second and sixthaspect or a combination of the target and outside regions 11 and 103 forthe step S27-4 or S28-5 in the fifth aspect to measure one or a set ofvalues or C_(m)

_(n) or C₁

₁-C

for each stop W_(m)

_(n) or C₁

₁-C

of the measuring pixels 20 of each stop of the two-dimensional movingwindow 2. Thereby, the values C_(m)

_(n)-C

may have the number of M

-by-N

to be measured from each stop of the two-dimensional moving window 2.

Referring to FIG. 35B, each stop of the measuring pixels 20 of each stopof the two-dimensional moving window 2 may have a profile defined by aprofile of a combination of multiple computation pixels P_(k)

_(l), arranged in an m

-by-N

array, of a two-dimensional computational map 12, wherein the number of“m

” may be an integer greater than or equal to 1, such as 2, 3 or 4, andthe number of “n

” may be an integer greater than or equal to 1, such as 2, 3 or 4. Inthis case, the number of “m

” is equal to 3 and the number “n

” is equal to 3, as seen in FIG. 35B.

FIGS. 35C-35K are schematic views showing a path of a two-dimensionalmoving windows in accordance with the present application. In the stepof moving the two-dimensional moving window 2 on the target region 11for the step S22-4 or S23-3 in the first, second and sixth aspect or acombination of the target and outside regions 11 and 103 for the stepS27-4 or S28-5 in the fifth aspect, once the two-dimensional movingwindow 2 moves step by step in a x direction with a shift equal to ax-direction width X_(fp) of the computation pixels P_(k)

_(l) of the two-dimensional computational map 12 by one or more steps ofthe number of (m_(cp)−1), the two-dimensional moving window 2 may jumpin the x direction with a shift equal to the x-direction width X_(fp)times the number of (m

−1). Once the two-dimensional moving window 2 moves row by row in a ydirection with a shift equal to a y-direction width Y_(fp) of thecomputation pixels P_(k)

_(l) of the two-dimensional computational map 12 by one or more rows ofthe number of n

, the two-dimensional moving window 2 may jump in the y direction with ashift equal to the y-direction width Y_(fp) times the number of n

.

For example, referring to FIGS. 35C-35K, in this case, thetwo-dimensional moving window 2 may be defined by the condition that thenumber of “M

” is equal to 2, the number “N_(mp)” is equal to 2, the number or “m

” is equal to 3 and the number “n

” is equal to 3, as seen in FIGS. 35A and 35B, the two-dimensionalmoving window 2 may move from the top left corner of the target region11 fur the step S22-4 or S23-3 in the first, second and sixth aspect ora combination of the target and outside regions 11 and 103 for the stepS27-4 or S28-5 in the fifth aspect, as seen in FIG. 35C to measure fouror four sets of values C

, C

, C

and C

for four respective stops W

, W

, W

and W

of the measuring pixels 20 of a stop of the two-dimensional movingwindow 2. Next, the two-dimensional moving window 2 may move rightwardsstep by step in a x direction with a shift equal to a x-direction widthX_(fp) of the computation pixels P_(k)

_(l) of the two-dimensional computational map 12, as seen in FIGS. 35Dand 35E, to measure four or four sets of values C

, C

, C

and C

for four respective stops W

, W

, W

and W

of the measuring pixels 20 of a first stop of the two-dimensional movingwindow 2 for the first step and to measure four or four sets of values C

, C

, C

and C

for four respective stops W

, W

, W

and W

of the measuring pixels 20 of a second stop of the two-dimensionalmoving window 2 for the second step. Once the two-dimensional movingwindow 2 moves rightwards step by step in the x direction with a shiftequal to the x-direction width X_(fp) by two steps, the two-dimensionalmoving window 2 may jump rightwards in the x direction with a shiftequal to the x-direction width X_(fp) times 4, as seen in FIG. 35F, tomeasure four or four sets of values C

, C

, C

and C

for four respective stops W

, W

, W

and W

of the measuring pixels 20 of a stop of the two-dimensional movingwindow 2.

Accordingly, in a step S35-1, the two-dimensional moving window may moverightwards step by step in the x direction with a shift equal to thex-direction width X_(fp) to measure four or four sets of values C

, C

, C

and C

for four respective stops W

, W

, W

and W

of the measuring pixels 20 of a first stop of the two-dimensional movingwindow 2 for the first step, wherein FX1=FX3=tx*M_(mp)*m_(cp)+2,FX2=FX4=tx*M_(mp)*m_(cp)+2, TY1=TY2=ty*N_(mp)*n_(cp)+1 andTY3=TY4=ty*N_(mp)*n_(cp)n_(cp)+1, wherein tx is the number of jumps ofthe two-dimensional moving window 2 in the x direction, and ty is thenumber of jumps of the two-dimensional moving window 2 in the ydirection, and to measure four or four sets of values C

, C

, C

and C

for four respective stops W

, W

, W

and W

of the measuring pixels 20 of the second stop of the two-dimensionalmoving window 2 for the second step, wherein SX1=SX3=tx*M_(mp)*m_(cp)+3and SX2=SX4=tx*M_(mp)*m_(cp)+m_(cp)+3. Once the two-dimensional movingwindow 2 moves rightwards step by step in the x direction with a shiftequal to the x-direction width X_(fp) by two steps, the two-dimensionalmoving window 2 may jump rightwards in the x direction with a shiftequal to the x-direction width X_(fp) times 4 to measure four or foursets of values C

, C

, C

and C

for four respective stops W

, W

, W

and W

of the measuring pixels 20 of a stop of the two-dimensional movingwindow 2, wherein TX1=TX3=tx*M_(mp)*m_(cp)+1 andTX2=TX4=tx*M_(mp)*m_(cp)+m_(cp)+1. The above step S35-1 may repeat untila stop of the two-dimensional moving window 2 has a stop of one of themeasuring pixels 20 reaching to a right side of the two-dimensionalcomputational map 12 as seen in FIG. 35G.

After a stop of the two-dimensional moving window 2 has a stop of one ofthe measuring pixels 20 reaching to a right side of the two-dimensionalcomputational map 12 in the step S35-1 as seen in FIG. 35, a step S35-2continues wherein the two-dimensional moving window 2 may move downwardsin a y-direction with a shift equal to a y-direction width Y_(fp) of thecomputation pixels P_(k)

_(l) of the two-dimensional computational map 12 and to a left side ofthe two-dimensional computational map 2, as seen in FIG. 35H, to measurefour or four sets of values C

, C

, C

and C

for four respective stops W

, W

, W

and W

of the measuring pixels 20 of a stop of the two-dimensional movingwindow 2, wherein FY1=FY2=ty*N_(mp)*n_(cp)+2 andFY3=FY4=ty*N_(mp)*n_(cp)+N_(cp)+2. Next, in a step S35-3, thetwo-dimensional moving window 2 may move rightwards step by step in thex direction with a shift equal to the x-direction width X_(fp) tomeasure four or four sets of values C

, C

, C

and C

for four respective stops W

, W

, W

and W

of the measuring pixels 20 of a first stop of the two-dimensional movingwindow 2 for the first step and to measure four or four sets of values C

, C

, C

and C

for four respective stops W

, W

, W

and W

of the measuring pixels 20 of the second stop of the two-dimensionalmoving window 2 for the second step. Once the two-dimensional movingwindow 2 moves rightwards step by step in the x direction with a shiftequal to the x-direction width X_(fp) by two steps, the two-dimensionalmoving window 2 may jump rightwards in the x direction with a shiftequal to the x-direction width X_(fp) times 4 to measure four or foursets of values C

, C

, C

and C

for four respective stops W

, W

, W

and W

of the measuring pixels 20 of a stop of the two-dimensional movingwindow 2. The above step S35-3 may repeat until a stop of thetwo-dimensional moving window 2 has a stop of one of the measuringpixels 20 reaching to the right side of the two-dimensionalcomputational map 12.

After a stop of the two-dimensional moving window 2 has a stop of one ofthe measuring pixels 20 reaching to a right side of the two-dimensionalcomputational map 12 in the step S35-3, a step S35-4 continues whereinthe two-dimensional moving window 2 may move downwards in a y-directionwith a shift equal to the y-direction width Y_(fp) of the computationpixels P_(k)

_(l) of the two-dimensional computational map 12 and to the left side ofthe two-dimensional computational map 2, as seen in FIG. 35I, to measurefour or four sets of values C

, C

, C

and C

for four respective stops W

, W

, W

and W

of the measuring pixels of a stop of the two-dimensional moving window2, wherein SY1=SY2=ty*N_(mp)*n_(cp)+3 andSY3=SY4=ty*N_(mp)*n_(cp)+n_(cp)+3. Next in a step S35-5, thetwo-dimensional moving window 2 may move rightwards step by step in thex direction with a shift equal to the x-direction width X_(fp) tomeasure four or four sets of values C

, C

, C

and C

for four respective stops W

, W

, W

and W

of the measuring pixels 20 of a first stop of the two-dimensional movingwindow 2 for the first step and to measure four or four sets of values C

, C

, C

and C

for four respective stops W

, W

, W

and W

of the measuring pixels 20 of the second stop of the two-dimensionalmoving window 2 for the second step. Once the two-dimensional movingwindow 2 moves rightwards step by step in the x direction with a shiftequal to the x-direction width X_(fp) by two steps, the two-dimensionalmoving window 2 may jump rightwards in the x direction with a shiftequal to the x-direction width X_(fp) times 4 to measure four or foursets of values C

, C

, C

and C

for four respective stops W

, W

, W

and W

of the measuring, pixels 20 of a stop of the two-dimensional movingwindow 2. The above step S35-5 may repeat until a stop of thetwo-dimensional moving window 2 has a stop of one of the measuringpixels 20 reaching to the right side of the two-dimensionalcomputational map 12.

Once the two-dimensional moving window 2 moves downwards row by row inthe y direction with a shift equal to the y-direction width Y_(fp) bythree rows, a step S35-6 continues wherein the two-dimensional movingwindow 2 may jump downwards in the y direction with a shift equal to they-direction width Y_(fp) times 3, as seen in FIG. 35J, to measure fouror four sets of values C

, C

, C

and C

for four respective stops W

, W

, W

and W

of the measuring pixels 20 of a stop of the two-dimensional movingwindow 2 Next, a loop of the steps S35-1 through S35-6 repeats until astop of the two-dimensional moving window 2 has a stop of one of themeasuring pixels 20 reaching to a bottom and right sides of thetwo-dimensional computational map 12 as seen in FIG. 35K.

The steps, features, benefits and advantages that have been discussedare merely illustrative. None of them, nor the discussions relating tothem, are intended to limit the scope of protection in any way. Numerousother embodiments are also contemplated. These include embodiments thathave fewer, additional, and/or different steps, features, benefits andadvantages, These also include embodiments in which the steps arearranged and/or ordered differently.

What is claimed is:
 1. A method for obtaining a probability of an eventin a three-dimensional probability map for a three-dimensionalstructure, comprising: providing, by an imaging system, a firstcomputation voxel, which is a three-dimensional unit of thethree-dimensional probability map, having a first dimension in a firstdirection, a second dimension in a second direction and a thirddimension in a third direction; obtaining, by the imaging system, atleast one value of at least one imaging parameter for each stop of athree-dimensional moving window, wherein a first and a second of thestops of the three-dimensional moving window are partially overlappedand are shifted from each other in the first direction by a distancesubstantially equal to the first dimension of the first computationvoxel, the first stop and a third of the stops of the three-dimensionalmoving window are partially overlapped and are shifted from each otherin the second direction by a distance substantially equal to the seconddimension of the first computation voxel, and the first stop and afourth of the stops of the three-dimensional moving window are partiallyoverlapped and are shifted from each other in the third direction by adistance substantially equal to the third dimension of the firstcomputation voxel; matching, by the imaging system, the at least onevalue of the at least one imaging parameter to a classifier to obtain afirst probability of the event for each stop of the three-dimensionalmoving window; and calculating, by the imaging system, a secondprobability of the event for the first computation voxel based oninformation associated with the first probabilities of the event for thefirst through fourth stops of the three-dimensional moving window. 2.The method of claim 1, wherein the three-dimensional structure comprisesa biological structure.
 3. The method of claim 1, wherein thethree-dimensional structure comprises a biopsy sample.
 4. The method ofclaim 1, wherein the three-dimensional moving window has a volumegreater than or equal to two times of a volume of the first computationvoxel.
 5. The method of claim 1, wherein the multiple imaging parameterscomprise various magnetic resonance imaging (MRI) parameters.
 6. Themethod of claim 5, wherein the multiple imaging parameters comprise T1parameter, T2 parameter and tau parameter.
 7. The method of claim 5,wherein the multiple imaging parameters comprise T1 parameter, T2parameter and K-trans parameter.
 8. The method of claim I, wherein themultiple imaging parameters comprise an X-ray computed tomographyparameter.
 9. The method of claim 1, wherein the multiple imagingparameters comprise an ultrasonic parameter.
 10. The method of claim 1,wherein the event comprises occurrence of a cancer.
 11. The method ofclaim 1, wherein said calculating the second probability of the eventfor the first computation voxel comprises: calculating, by the imagingsystem, a first assumed probability of the event for the firstcomputation voxel based on information associated with the firstprobabilities of the event for the first through fourth stops of thethree-dimensional moving window; calculating, by the imaging system, asecond assumed probability of the event for each of other computationvoxels, other than the first computation voxel, in each of the firstthrough fourth stops, comprising said calculating the second assumedprobability of the event for a voxel of the other computation voxels ineach of the first through fourth stops based on information associatedwith the first probability of the event for each of the stops of thethree-dimensional moving window covering the voxel of the othercomputation voxels; calculating, by the imaging system, a probabilityguess of the event for each stop of the first through fourth stops ofthe three-dimensional moving window, comprising said calculating theprobability guess of the event for a stop of the first through fourthstops of the three-dimensional moving window based on informationassociated with the first assumed probability of the event for the firstcomputation voxel and the second assumed probabilities of the event forthe other computation voxels in the stop of the first through fourthstops; calculating, by the imaging system, a difference between theprobability guess of the event and the first probability of the eventfor each of the first through fourth stops of the three-dimensionalmoving window; and updating, by the imaging system, the first assumedprobability of the event for the first computation voxel based oninformation associated with the difference for each of the first throughfourth stops of the three-dimensional moving window.
 12. The method ofclaim 11, wherein said updating the first assumed probability of theevent for the first computation voxel further comprises: calculating, bythe imaging system, each of error correction contributions from thefirst through fourth stops of the three-dimensional moving window to thefirst computation voxel by multiplying the difference for each of thefirst through fourth stops of the three-dimensional moving window by aratio of a volume of the first computation voxel to a volume of thethree-dimensional moving window; calculating, by the imaging system, anerror correction factor (ECF) for the first computation voxel by summingthe error correction contributions; and subtracting, by the imagingsystem, the error correction factor (ECF) for the first computationvoxel from the first assumed probability of the event for the firstcomputation voxel.
 13. The method of claim 1 further comprising:providing, by the imaging system, a fifth of the stops of thethree-dimensional moving window covering a second computation voxel,wherein the second computation voxel is another three-dimensional unitof the three-dimensional probability map, having the first dimension inthe first direction, the second dimension in the second direction andthe third dimension in the third direction; calculating, by the imagingsystem, a difference between the first probability of the event for thefifth stop and the first probability of the event for each of all itsneighboring stops of the three-dimensional moving window partiallyoverlapping the fifth stop of the three-dimensional moving window;calculating, by the imaging system, a ratio of each of the differencesto the first probability of the event for the fifth stop of thethree-dimensional moving window; determining, by the imaging system, ifeach of absolute values of the ratios is less than or equal to athreshold value; defining, by the imaging system, a space covered by thefifth stop and all its neighboring stops partially overlapping the fifthstop of the three-dimensional moving window as a uniform space, whereinthe second computation voxel is in the uniform space; assigning, by theimaging system, a constant probability of the event for the secondcomputation voxel, wherein the constant probability of the event isassociated with the first probability of the event for the fifth stopand the first probabilities of the event for all its neighboring stopspartially overlapping the fifth stop of the three-dimensional movingwindow; and assigning, by the imaging system, the constant probabilityof the event for each of other computation voxels, other than the secondcomputation voxel, in the uniform space.
 14. The method of claim 13comprising said calculating the second probability of the event for thefirst computation voxel based on further information associated with athird probability of the event for a sixth of the stops of thethree-dimensional moving window partially overlapping the uniform space,wherein the third probability of the event for the sixth stop of thethree-dimensional moving window is calculated based on informationassociated with the constant probability of the event for eachcomputation voxel in the uniform space and in the sixth stop.
 15. Themethod of claim 13, wherein said calculating the second probability ofthe event for the first computation voxel comprises: calculating, by theimaging system, a first assumed probability of the event for the firstcomputation voxel based on information associated with the firstprobabilities of the event for the first through fourth stops of thethree-dimensional moving window; calculating, by the imaging system, asecond assumed probability of the event for each of other computationvoxels, other than the first computation voxel, in each of the firstthrough fourth stops, comprising said calculating the second assumedprobability of the event for a voxel of the other computation voxels ineach of the first through fourth stops based on information associatedwith the first probability of the event for each of the stops of thethree-dimensional moving window covering the voxel of the othercomputation voxels; calculating, by the imaging system, a firstprobability guess of the event for a certain stop of the first throughfourth stops of the three-dimensional moving window partiallyoverlapping the uniform space based on information associated with thefirst assumed probability of the event for the first computation voxel,the second assumed probability of the event for each of the othercomputation voxels in the certain stop and outside the uniform space andthe constant probability of the event for the other computation voxelsin the certain stop and in the uniform space; calculating, by theimaging system, a second probability guess of the event for each ofother stops, other than the certain stop, of the first through fourthstops not overlapping the uniform space, comprising said calculating thesecond probability guess of the event for a stop of the other stops ofthe first through fourth stops not overlapping the uniform space basedon information associated with the first assumed probability of theevent for the first computation voxel and the second assumed probabilityof the event for each of the other computation voxels outside theuniform space and in the stop of the other stops; calculating, by theimaging system, a first difference between the first probability guessof the event and the first probability of the event for the certainstop; calculating, by the imaging system, a second difference betweenthe second probability guess of the event and the first probability ofthe event for each of the other stops of the first through fourth stopsnot overlapping the uniform space; and updating, by the imaging system,the first assumed probability of the event for the first computationvoxel based on information associated with the first difference and thesecond differences for the first through fourth stops of thethree-dimensional moving window.
 16. The method of claim 1, wherein theclassifier comprises a Bayesian classifier.
 17. The method of claim 1,wherein the first and second directions are substantially perpendicularto each other, the first and third directions are substantiallyperpendicular to each other and the second and third directions aresubstantially perpendicular to each other.
 18. A method for obtaining avalue in a three-dimensional computational map for a three-dimensionalstructure, comprising: providing, by an imaging system, a firstcomputation voxel, which is a three-dimensional unit of thethree-dimensional computational map, having a first dimension in a firstdirection, a second dimension in a second direction and a thirddimension in a third direction; obtaining, by the imaging system, afirst value of an imaging parameter for each stop of a three-dimensionalmoving window, wherein a first and a second of the stops of thethree-dimensional moving window are partially overlapped and are shiftedfrom each other in the first direction by a distance substantially equalto the first dimension of the first computation voxel, the first stopand a third of the stops of the three-dimensional moving window arepartially overlapped and are shifted from each other in the seconddirection by a distance substantially equal to the second dimension ofthe first computation voxel, and the first stop and a fourth of thestops of the three-dimensional moving window are partially overlappedand are shifted from each other in the third direction by a distancesubstantially equal to the third dimension of the first computationvoxel; and calculating, by the imaging system, a second value of theimaging parameter for the first computation voxel based on informationassociated with the first values for the first through fourth stops ofthe three-dimensional moving window.
 19. The method of claim 18, whereinthe three-dimensional structure comprises a biological structure. 20.The method of claim 18, wherein the three-dimensional structurecomprises a biopsy sample.
 21. The method of claim 18, wherein thethree-dimensional moving window has a volume greater than or equal totwo times of a volume of the first computation voxel.
 22. The method ofclaim 18, wherein the imaging parameter comprises a magnetic resonanceimaging (MRI) parameter.
 23. The method of claim 18, wherein the imagingparameter comprises a X-ray computed tomography parameter.
 24. Themethod of claim 18, wherein the imaging parameter comprises anultrasonic parameter.
 25. The method of claim 18, wherein the imagingparameter comprises an infrared absorbance parameter.
 26. The method ofclaim 18, wherein said calculating the second value of the imagingparameter for the first computation voxel comprises: calculating, by theimaging system, a first assumed value of the imaging parameter for thefirst computation voxel based on information associated with the firstvalues for the first through fourth stops of the three-dimensionalmoving window; calculating, by the imaging system, a second assumedvalue of the imaging parameter for each of other computation voxels,other than the first computation voxel, in each of the first throughfourth stops, comprising said calculating the second assumed value for avoxel of the other computation voxels in each of the first throughfourth stops based on information associated with the first value foreach of the stops of the three-dimensional moving window covering thevoxel of the other computation voxels; calculating, by the imagingsystem, a value guess of the imaging parameter for each of the firstthrough fourth stops of the three-dimensional moving window, comprisingsaid calculating the value guess for a stop of the first through fourthstops of the three-dimensional moving window based on informationassociated with the first assumed value for the first computation voxeland the second assumed values for the other computation voxels in thestop of the first through fourth stops; calculating, by the imagingsystem, a difference between the value guess and the first value foreach of the first through fourth stops of the three-dimensional movingwindow; and updating, by the imaging system, the first assumed value forthe first computation voxel based on information associated with thedifference for each of the first through fourth stops of thethree-dimensional moving window.
 27. The method of claim 26, whereinsaid updating the first assumed value for the first computation voxelfurther comprises: calculating, by the imaging system, each of errorcorrection contributions from the first through fourth stops of thethree-dimensional moving window to the first computation voxel bymultiplying the difference for each of the first through fourth stops ofthe three-dimensional moving window by a ratio of a volume of the firstcomputation voxel to a volume of the three-dimensional moving window;calculating, by the imaging system, an error correction factor (ECF) forthe first computation voxel by summing the error correctioncontributions; and subtracting, by the imaging system, the errorcorrection factor (ECF) for the first computation voxel from the firstassumed value for the first computation voxel.
 28. The method of claim18 further comprising: providing, by the imaging system, a fifth of thestops of the three-dimensional moving window covering a secondcomputation voxel, wherein the second computation voxel is anotherthree-dimensional unit of the three-dimensional computational map,having the first dimension in the first direction, the second dimensionin the second direction and the third dimension in the third direction;calculating, by the imaging system, a difference between the first valuefor the fifth stop and the first value for each of all its neighboringstops of the three-dimensional moving window partially overlapping thefifth stop of the three-dimensional moving window; calculating, by theimaging system, a ratio of each of the differences to the first valuefor the fifth stop of the three-dimensional moving window; determining,by the imaging system, if each of absolute values of the ratios is lessthan or equal to a threshold value; defining, by the imaging system, aspace covered by the fifth stop and all its neighboring stops partiallyoverlapping the fifth stop of the three-dimensional moving window as auniform space, wherein the second computation voxel is in the uniformspace; assigning, by the imaging system, a constant value of the imagingparameter for the second computation voxel, wherein the constant valueis associated with the first value for the fifth stop and the firstvalues for all its neighboring stops partially overlapping the fifthstop of the three-dimensional moving window; and assigning, by theimaging system, the constant value for each of other computation voxels,other than the second computation voxel, in the uniform space.
 29. Themethod of claim 28 comprising said calculating the second value for thefirst computation voxel based on further information associated with athird value of the imaging parameter for a sixth of the stops of thethree-dimensional moving window partially overlapping the uniform space,wherein the third value for the sixth stop of the three-dimensionalmoving window is calculated based on information associated with theconstant value for each computation voxel in the uniform space and inthe sixth stop.
 30. The method of claim 28, wherein said calculating thesecond value for the first computation voxel comprises: calculating, bythe imaging system, a first assumed value of the imaging parameter forthe first computation voxel based on information associated with thefirst values for the first through fourth stops of the three-dimensionalmoving window; calculating, by the imaging system, a second assumedvalue of the imaging parameter for each of other computation voxels,other than the first computation voxel, in each of the first throughfourth stops, comprising said calculating the second assumed value for avoxel of the other computation voxels in each of the first throughfourth stops based on information associated with the first value foreach of the stops of the three-dimensional moving window covering thevoxel of the other computation voxels; calculating, by the imagingsystem, a first value guess of the imaging parameter for a certain stopof the first through fourth stops of the three-dimensional moving windowpartially overlapping the uniform space based on information associatedwith the first assumed value for the first computation voxel, the secondassumed value for each of the other computation voxels in the certainstop and outside the uniform space and the constant value for the othercomputation voxels in the certain stop and in the uniform space;calculating, by the imaging system, a second value guess of the imagingparameter for each of other stops, other than the certain stop, of thefirst through fourth stops not overlapping the uniform space, comprisingsaid calculating the second value guess for a stop of the other stops ofthe first through fourth stops not overlapping the uniform space basedon information associated with the first assumed value for the firstcomputation voxel and the second assumed value for each of the othercomputation voxels outside the uniform space and in the stop of theother stops; calculating, by the imaging system, a first differencebetween the first value guess of the event and the first value for thecertain stop; calculating, by the imaging system, a second differencebetween the second value guess and the first value for each of the otherstops of the first through fourth stops not overlapping the uniformspace; and updating, by the imaging system, the first assumed value forthe first computation voxel based on information associated with thefirst difference and the second differences for the first through fourthstops of the three-dimensional moving window.
 31. The method of claim18, wherein the first and second directions are substantiallyperpendicular to each other, the first and third directions aresubstantially perpendicular to each other and the second and thirddirections are substantially perpendicular to each other.